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Complete experiments: oscillations.

Capstone 'EX' experiments include all the apparatus, sensors (when needed), manuals, and PASCO Capstone files you'll need in your student physics lab.

Grade Level: College

Subject: Physics

01) Large Amplitude Pendulum

This experiment explores the dependence of the period of a simple pendulum on the amplitude of the oscillation. Also, the angular displacement, angular velocity, and angular acceleration for large amplitude are plotted versus time to show the difference from the sinusoidal motion of low amplitude oscillations. The student uses calculus to quantitatively see the relationships between the angular displacement, angular velocity, and angular acceleration curves.

02) Physical Pendulum - Period and Inertia

Period - This experiment explores the dependence of the period of a physical pendulum (a uniform bar) on the distance between the pivot point and the center of mass of the physical pendulum. Rotational Inertia - The period of oscillation of a physical pendulum will be measured and used to calculate the rotational inertia of the pendulum. The rotational inertia is also determined by measuring the mass and the dimensions of the pendulum.

03) Variable-g Pendulum

This experiment explores the dependence of the period of a simple pendulum on the acceleration due to gravity.

04) Physical Pendulum Period and Inertia

This experiment has two parts: 1. Period of a Thin Rod explores the dependence of the period of a physical pendulum (a uniform bar) on the distance between the pivot point and the center of mass of the physical pendulum. 2. In Physical Pendulum Rotational Inertia, the period of oscillation of a physical pendulum will be measured and used to calculate the rotational inertia of the pendulum. The rotational inertia is also determined by measuring the mass and the dimensions of the pendulum.

05) Physical Pendulum Period - Wireless

06) driven damped cart oscillations.

The oscillator consists of a Smart Cart attached to two springs. The damping is provided by magnets mounted on the Smart Cart that cause eddy currents in the aluminum track. The amplitude of the oscillation is plotted versus the driving frequency for different amounts of magnetic damping. Increased damping is provided by moving adjustable magnets closer to the aluminum track.

07) Driven Damped Harmonic Oscillations

The oscillator consists of an aluminum disk with a pulley that has a string wrapped around it to two springs. The angular positions and velocities of the disk and the driver are recorded as a function of time using two Rotary Motion Sensors. The amplitude of the oscillation is plotted versus the driving frequency for different amounts of magnetic damping. Increased damping is provided by moving an adjustable magnet closer to the aluminum disk.

08) Coupled Pendulum

Two pendula are coupled by a spring. This system has two natural modes: 1. The two pendula swing in phase with each other. 2. The two pendula swing 180 degrees out of phase. When one of the pendula is held at rest and the other is set oscillating, the energy of the oscillating pendulum is transferred to the other pendulum by the spring. The period of the energy transfer can be predicted and verified by experiment.

The chaotic behavior of driven nonlinear pendulum is explored by graphing its motion in phase space and by making a Poincare plot. These plots are compared to the motion of the pendulum when it is not chaotic.

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Experiment Features

Teacher files, sparkvue files, pasco capstone files, wireless sensors, pasport sensors, scienceworkshop sensors.

Many lab activities can be conducted with our Wireless , PASPORT , or even ScienceWorkshop sensors and equipment. For assistance with substituting compatible instruments, contact PASCO Technical Support . We're here to help.

An Accurate Simple Harmonic Oscillator Laboratory

Learning Objectives * Execute a specific experimental procedure to test a specific hypothesis. * Use the Tracker video analysis software for a simple experiment. * Analyze the acquired data with a spreadsheet to test the hypothesis. * Explain in one’s own words whether the experimental data supported the hypothesis, and (if so), how well. *Use a carefully measured physical quantity from one experiment (the spring constant from Hooke’s Law) to predict an important quantity in a different experiment (the period in the Simple Harmonic Oscillator ).  See:  https://www.physicsforums.com/insights/an-accurate-hookes-law-laboratory/

Introduction Understanding the simple harmonic oscillator is an essential building block for describing a wide array of physical systems including most things that vibrate, radiate, or oscillate. A straightforward experimental realization of the simple harmonic oscillator is a mass suspended from a spring. When displaced downward a short distance from its equilibrium position and released, the mass will oscillate up and down repeatedly. The period of this motion is independent of the amplitude of the oscillation and it is predicted by a simple formula. Hypothesis: The period of a simple harmonic oscillator constructed by a mass on a spring is given by T = 2 π (m/k) 1/2 , where m is the mass (in kg) and k is the spring constant (in N/m). The strategy to test this hypothesis is to construct a simple harmonic oscillator with a mass and spring and measure its period using Tracker to see how long it takes to complete 10 full oscillations up and down. The spring constant should have been obtained in the earlier experiment on Hooke’s Law. Due care should be taken to use the same spring in both experiments.

Method Materials * 1 video camera with file format compatible with Tracker – most cell phone cameras will work as well camcorders * Free Tracker video analysis program: https://physlets.org/tracker/

* The same spring that was used for the Hooke’s Law experiment * A range of test masses (4) that can be hung from the spring. Masses should have a range of values so that the heaviest mass is 3-4 times the lightest mass, and the range has (approximately) equal steps over the interval. Some of the same masses used in the Hooke’s Law experiment would be ideal.

* A rigid hook, bar, rod, or other support from which spring may be suspended as masses are hung. * A lab notebook for recording data. * A computer, plotting program, and spreadsheet for analyzing data.

Procedure for Experiment

Be intentional about planning masses for this experiment. The video analysis will measure the period to 1/300th of a second or so. Several factors will contribute to your experimental uncertainties. Uncertainties in the video analysis will yield small uncertainties in the period determination. Selecting 4 masses at the heavier end of what you have available will yield longer periods such that the relative error of a given fraction of a second is smaller. Uncertainties in the measurements of your masses will yield uncertainties in your predicted periods, as will uncertainty in your determination of the spring constant from your Hooke’s Law experiment. Prepare a new page in your lab notebook, putting the date and title of the lab at the top of a new page. Write the value of the spring constant, k, near the top. Include at least 4 decimal places and the units. Your Hooke’s Law lab should have measured Force in Newtons and spring position in meters, so the slope of the line (rise over run) has units of N/m (Newtons per meter). Double-check all this and record the spring constant k something like k = 18.31161 N/m. (Your number will be different.) Now, make two new columns below that for the original data of this experiment. The first column is mass (g); the second column is 10T (s). The 10 T represents the time for 10 periods that you will determine from video analysis. Set up the video camera pointed at the mass and spring. You need a level of zoom so the video catches the complete range of motion, but you don’t want lots of space in your field of view outside the motion of the test mass. The camera orientation and zoom level may need to be adjusted between test masses. Now, use your electronic balance to determine the mass of your first test mass. This mass needs to be heavy enough to stretch your spring significantly without hitting the table or support. Now, pull the mass downward a few cm and release it. It should oscillate up and down in the spring. It may take a few tries, but you want the dominant motion to be a simple up and down with minimal side to side motion. If there is much side-to-side motion, stop the mass and try again. Once you have the up and down motion you want, start the video camera and record at least 10 full oscillations. You may want to record 12-15 so you are sure you have 10 complete oscillations to analyze on the video. Once you have your first video recorded, replace the mass with a different one and repeat for all four of your test masses, so you end up with four videos, one with each test mass. The pan and zoom of your video camera may need to be adjusted between masses, as heavier masses will hang lower. Procedure for Analysis Transfer the video from the camera to a computer and open a video in the Tracker program. Move forward to the frame just corresponding to the very lowest point on the first recorded oscillation. You may need to step the video forward and back to find just the right frame. When you find the frame corresponding to the furthest motion of mass downward, set the time to zero for that frame. (Note, since the Tracker program is only used for timing, no length scale calibration is needed.) Now, let the video play forward for 10 complete oscillations (up and down) from where you set time to zero. Stop the video and move frame by frame until you find the frame corresponding most closely to the mass reaching its extremely low position on the 10 th oscillation. Record that time in your lab notebook as 10T (ten times the period). The period of the simple harmonic oscillator is the time to bounce up and down 1 time. You allowed the mass to bounce up and down 10 times to increase accuracy. The period, T, can be obtained by dividing the measured 10T by 10. Now, the measured period can be compared with the predicted period and a relative error computed.

Set up columns in your analysis spreadsheet like in Table 1. You will need the spring constant, k, for some calculations, so enter it in a cell near the top. The two leftmost columns [mass (g) and 10 T (s)] should contain your raw data, exactly as you wrote it in your lab notebook. The third column should be the mass converted to kg (divide by 1000 to convert g to kg). The fourth column should be the measured period, T, computed by dividing the measured 10 T by 10. The fifth column should be the predicted period, T, for each mass, computed with a spreadsheet formula like =2*3.1415926*SQRT(C5/$D$1), assuming the spring constant, k, is in element D1 and the mass in kg is in element C5. Note the $D$1 will allow the formula to be pasted into lower cells in the same column and keep the reference to the cell with k. The sixth column contains the relative error between the predicted and measured periods computed as the (Predicted T – Measured T)/Measured T, or =(E5 – D5)/D5.

Figure 1: Period T vs. Mass Predictions and measured data for the simple harmonic oscillator.

Results (50 points total) Your results should include a table containing your measured 10T, the predicted period, the measured period, and the relative error in the prediction. Make sure to record things according to the experiment you performed rather than the example in the instructions or how you think things should have gone. If there is a major discrepancy between your predicted and measured values, you may retrace your steps and try and find where you made the error. The most likely sources of error over 2% are errors in measuring the period, entering wrong values, or an error measuring the spring constant. Discussion (50 points total) Your written discussion should be from 1 to 3 paragraphs discussing the following questions in complete sentences: * Was your hypothesis supported? Why or why not? How strong is the support for the hypothesis? (20 points) * How much would you need to increase the mass to double the period? (10 points) * Estimate the period of a simple harmonic oscillator with a spring constant double the one for yours and a mass of 100g. (10 points)

* Estimate the mass of a simple harmonic oscillator with your spring constant and a period of 1.000 s. (10 points)

I grew up working in bars and restaurants in New Orleans and viewed education as a path to escape menial and dangerous work environments, majoring in Physics at LSU. After being a finalist for the Rhodes Scholarship I was offered graduate research fellowships from both Princeton and MIT, completing a PhD in Physics from MIT in 1995. I have published papers in theoretical astrophysics, experimental atomic physics, chaos theory, quantum theory, acoustics, ballistics, traumatic brain injury, epistemology, and education.

My philosophy of education emphasizes the tremendous potential for accomplishment in each individual and that achieving that potential requires efforts in a broad range of disciplines including music, art, poetry, history, literature, science, math, and athletics. As a younger man, I enjoyed playing basketball and Ultimate. Now I play tennis and mountain bike 2000 miles a year.

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Including tracking software into education needs to be promoted more. Back in high-school I did a similar experiment with a wheel and a VCR to prove to my teacher that the height of a point on the perimiter as a function of time was a sinusoid, not a cycloid (that’s as a function of horizontal displacement). I still recall going frame by frame.Agreed. With some careful experimental design, getting accurate results with Tracker is just so easy with little more than a video camera and a computer.

Requires students to be able to count to ten. Effectively unusable. :rolleyes:

Just kidding. Even today it is a good experiment. Including tracking software into education needs to be promoted more. Back in high-school I did a similar experiment with a wheel and a VCR to prove to my teacher that the height of a point on the perimiter as a function of time was a sinusoid, not a cycloid (that’s as a function of horizontal displacement). I still recall going frame by frame.

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• Science Clarified
• Real-Life Physics Vol 2
• Oscillation

Oscillation - Real-life applications

Springs and damping.

Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.

If one were to jump on a piece of trampoline fabric stretched across an ordinary table—one with no springs—the experience would not be much fun, because there would be little bounce. On the other hand, the elastic potential energy of the trampoline's springs ensures that anyone of normal weight who jumps on the trampoline is liable to bounce some distance into the air. As a person's body comes down onto the trampoline fabric, this stretches the fabric (itself highly elastic) and, hence, the springs. Pulled from a position of equilibrium, the springs acquire elastic potential energy, and this energy makes possible the upward bounce.

As a car goes over a bump, the spring in its shock-absorber assembly is compressed, but the elastic potential energy of the spring immediately forces it back to a position of equilibrium, thus ensuring that the bump is not felt throughout the entire vehicle. However, springs alone would make for a bouncy ride; hence, a modern vehicle also has shock absorbers. The shock absorber, a cylinder in which a piston pushes down on a quantity of oil, acts as a damper—that is, an inhibitor of the springs' oscillation.

SIMPLE HARMONIC MOTION AND DAMPING.

Simple harmonic motion occurs when a particle or object moves back and forth within a stable equilibrium position under the influence of a restoring force proportional to its displacement. In an ideal situation, where friction played no part, an object would continue to oscillate indefinitely.

Of course, objects in the real world do not experience perpetual oscillation; instead, most oscillating particles are subject to damping, or the dissipation of energy, primarily as a result of friction. In the earlier illustration of the spring suspended from a ceiling, if the string is pulled to a position of maximum displacement and then released, it will, of course, behave dramatically at first. Over time, however, its movements will become slower and slower, because of the damping effect of frictional forces.

HOW DAMPING WORKS.

When the spring is first released, most likely it will fly upward with so much kinetic energy that it will, quite literally, bounce off the ceiling. But with each transit within the position of equilibrium, the friction produced by contact between the metal spring and the air, and by contact between molecules within the spring itself, will gradually reduce the energy that gives it movement. In time, it will come to a stop.

If the damping effect is small, the amplitude will gradually decrease, as the object continues to oscillate, until eventually oscillation ceases. On the other hand, the object may be "overdamped," such that it completes only a few cycles before ceasing to oscillate altogether. In the spring illustration, overdamping would occur if one were to grab the spring on a downward cycle, then slowly let it go, such that it no longer bounced.

There is a type of damping less forceful than overdamping, but not so gradual as the slow dissipation of energy due to frictional forces alone. This is called critical damping. In a critically damped oscillator, the oscillating material is made to return to equilibrium as quickly as possible without oscillating. An example of a critically damped oscillator is the shock-absorber assembly described earlier.

Even without its shock absorbers, the springs in a car would be subject to some degree of damping that would eventually bring a halt to their oscillation; but because this damping is of a very gradual nature, their tendency is to continue oscillating more or less evenly. Over time, of course, the friction in the springs would wear down their energy and bring an end to their oscillation, but by then, the car would most likely have hit another bump. Therefore, it makes sense to apply critical damping to the oscillation of the springs by using shock absorbers.

Bungee Cords and Rubber Bands

Many objects in daily life oscillate in a spring-like way, yet people do not commonly associate them with springs. For example, a rubber band, which behaves very much like a spring, possesses high elastic potential energy. It will oscillate when stretched from a position of stable equilibrium.

Rubber is composed of long, thin molecules called polymers, which are arranged side by side. The chemical bonds between the atoms in a polymer are flexible and tend to rotate, producing kinks and loops along the length of the molecule. The super-elastic polymers in rubber are called elastomers, and when a piece of rubber is pulled, the kinks and loops in the elastomers straighten.

The structure of rubber gives it a high degree of elastic potential energy, and in order to stretch rubber to maximum displacement, there is a powerful restoring force that must be overcome. This can be illustrated if a rubber band is attached to a ceiling, like the spring in the earlier example, and allowed to hang downward. If it is pulled down and released, it will behave much as the spring did.

The oscillation of a rubber band will be even more appreciable if a weight is attached to the "free" end—that is, the end hanging downward. This is equivalent, on a small scale, to a bungee jumper attached to a cord. The type of cord used for bungee jumping is highly elastic; otherwise, the sport would be even more dangerous than it already is. Because of the cord's elasticity, when the bungee jumper "reaches the end of his rope," he bounces back up. At a certain point, he begins to fall again, then bounces back up, and so on, oscillating until he reaches the point of stable equilibrium.

The Pendulum

As noted earlier, a pendulum operates in much the same way as a swing; the difference between them is primarily one of purpose. A swing exists to give pleasure to a child, or a certain bittersweet pleasure to an adult reliving a childhood experience. A pendulum, on the other hand, is not for play; it performs the function of providing a reading, or measurement.

One type of pendulum is a metronome, which registers the tempo or speed of music. Housed in a hollow box shaped like a pyramid, a metronome consists of a pendulum attached to a sliding weight, with a fixed weight attached to the bottom end of the pendulum. It includes a number scale indicating the number of oscillations per minute, and by moving the upper weight, one can change the beat to be indicated.

ZHANG HENG'S SEISMO-SCOPE.

Metronomes were developed in the early nineteenth century, but, by then, the concept of a pendulum was already old. In the second century A.D. , Chinese mathematician and astronomer Zhang Heng (78-139) used a pendulum to develop the world's first seismoscope, an instrument for measuring motion on Earth's surface as a result of earthquakes.

Zhang Heng's seismoscope, which he unveiled in 132 A.D. , consisted of a cylinder surrounded by bronze dragons with frogs (also made of bronze) beneath. When the earth shook, a ball would drop from a dragon's mouth into that of a frog, making a noise. The number of balls released, and the direction in which they fell, indicated the magnitude and location of the seismic disruption.

CLOCKS, SCIENTIFIC INSTRUMENTS, AND "FAX MACHINE".

In 718 A.D. , during a period of intellectual flowering that attended the early T'ang Dynasty (618-907), a Buddhist monk named I-hsing and a military engineer named Liang Ling-tsan built an astronomical clock using a pendulum. Many clocks today—for example, the stately and imposing "grandfather clock" found in some homes—like-wise, use a pendulum to mark time.

Physicists of the early modern era used pendula (the plural of pendulum) for a number of interesting purposes, including calculations regarding gravitational force. Experiments with pendula by Galileo Galilei (1564-1642) led to the creation of the mechanical pendulum clock—the grandfather clock, that is—by distinguished Dutch physicist and astronomer Christiaan Huygens (1629-1695).

In the nineteenth century, A Scottish inventor named Alexander Bain (1810-1877) even used a pendulum to create the first "fax machine." Using matching pendulum transmitters and receivers that sent and received electrical impulses, he created a crude device that, at the time, seemed to have little practical purpose. In fact, Bain's "fax machine," invented in 1840, was more than a century ahead of its time.

THE FOUCAULT PENDULUM.

By far the most important experiments with pendula during the nineteenth century, however, were those of the French physicist Jean Bernard Leon Foucault (1819-1868). Swinging a heavy iron ball from a wire more than 200 ft (61 m) in length, he was able to demonstrate that Earth rotates on its axis.

Foucault conducted his famous demonstration in the Panthéon, a large domed building in Paris named after the ancient Pantheon of Rome. He arranged to have sand placed on the floor of the Panthéon, and placed a pin on the bottom of the iron ball, so that it would mark the sand as the pendulum moved. A pendulum in oscillation maintains its orientation, yet the Foucault pendulum (as it came to be called) seemed to be shifting continually toward the right, as indicated by the marks in the sand.

The confusion related to reference point: since Earth's rotation is not something that can be perceived with the senses, it was natural to assume that the pendulum itself was changing orientation—or rather, that only the pendulum was moving. In fact, the path of Foucault's pendulum did not vary nearly as much as it seemed. Earth itself was moving beneath the pendulum, providing an additional force which caused the pendulum's plane of oscillation to rotate.

WHERE TO LEARN MORE

Brynie, Faith Hickman. Six-Minute Science Experiments. Illustrated by Kim Whittingham. New York: Sterling Publishing Company, 1996.

Ehrlich, Robert. Turning the World Inside Out, and 174 Other Simple Physics Demonstrations. Princeton, N.J.: Princeton University Press, 1990.

"Foucault Pendulum" Smithsonian Institution FAQs (Website). <http://www.si.edu/resource/faq/nmah/pendulum.html> (April 23, 2001).

Kruszelnicki, Karl S. The Foucault Pendulum (Web site). <http://www.abc.net.au/surf/pendulum/pendulum.html> (April 23, 2001).

Schaefer, Lola M. Back and Forth. Edited by Gail Saunders-Smith; P. W. Hammer, consultant. Mankato, MN: Pebble Books, 2000.

Shirley, Jean. Galileo. Illustrated by Raymond Renard. St. Louis: McGraw-Hill, 1967.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

Topp, Patricia. This Strange Quantum World and You. Nevada City, CA: Blue Dolphin, 1999.

Zubrowski, Bernie. Making Waves: Finding Out About Rhythmic Motion. Illustrated by Roy Doty. New York: Morrow Junior Books, 1994.

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Simple Pendulum: Theory, Experiment, Types & Derivation

Simple Pendulum: A simple pendulum device is represented as the point mass attached to a light inextensible string and suspended from a fixed support. A simple pendulum shows periodic motion, and it occurs in the vertical plane and is mainly driven by the gravitational force.

Ever wondered why an oscillating pendulum doesn’t slow down? Or what will happen to the time period of the simple pendulum when the displacement of the bob is increased? Will it increase as the distance required to cover to complete the oscillation increases, or will it decrease as the speed at the mean position increases, or will the speed compensate for the increased distance leaving the time period unchanged? What is the difference between a physical pendulum and a simple pendulum? There are a lot of questions about the motion of a simple pendulum. Let’s read further to find out the answers.

What is Called a Simple Pendulum?

A simple pendulum is a mechanical system of mass attached to a long massless inextensible string that performs oscillatory motion. Pendulums were used to keep a track of time in ancient days. The pendulum is also used for identifying the beats.

SHM or Simple Harmonic Motion

SHM or simple harmonic motion is the type of periodic motion in which the magnitude of restoring force on the body performing SHM is directly proportional to the displacement from the mean position but the direction of force is opposite to the direction of displacement. For SHM, \(F = – K{x^n}\) The value of ‘\(n\)’ is \(1\).

Thus the acceleration of the particle is given by, \(a = \frac{F}{m}\) \(a = \frac{{ – Kx}}{m}\) Where, \(m\) is the mass of the particle. Let \({\omega ^2} = \frac{K}{m}\) As, \(\frac{K}{m}\) is a positive constant. \( \Rightarrow \,\,a = – {\omega ^2}x\) \(\omega \) is known as angular frequency of the SHM. The time period of the Simple harmonic motion is given by, \(T = \frac{{2\pi }}{\omega }\)

Following are examples of example of the simple pendulums:

Oscillating Simple Pendulum: Calculation of Time Period

It is interesting to note that the oscillation of a simple pendulum can only be considered to be a simple harmonic motion when the oscillation is small or the amplitude of oscillation is very small as compared to two lengths of the string then by using small-angle approximation the motion of a simple pendulum is considered a simple harmonic motion. When the bob is displaced by some angle then the pendulum starts the periodic motion and for small value of angle of displacement the periodic motion is simple harmonic motion with the angular displacement of the bob.

Practice Exam Questions

\(F = mg\,{\rm{sin}}\left( \theta \right)\) \(a = g\,{\rm{sin}}\left( \theta \right)\) Here \(g\) is acceleration due to gravity. For small oscillation, \(\theta \) will be small, \({\rm{sin}}\left( \theta \right) = \theta = \frac{x}{l}\) Here \(x\) is the very small linear displacement of the bob corresponding to the displaced angle. \( \Rightarrow \,\,a = g\theta \) \( \Rightarrow \,\,a = g\frac{x}{l}\) Thus the angular frequency is given by, \( \Rightarrow \,\,{\omega ^2} = \frac{g}{l}\) The time period of the pendulum is given by, \(T = \frac{{2\pi }}{\omega }\) \( \Rightarrow \,\,T = 2\pi \sqrt {\frac{l}{g}} \) Thus from the expression for a time period of a simple pendulum, we can infer that the time period does not depend on the mass of the Bob at nor varies with the change in the small amplitude of the oscillation it only depends on the length of the string and acceleration due to this property it was widely used to keep a track of fixed interval of time does it helped the musicians to be on beats

Motion of Simple Pendulum: Effect of Gravity

As the time period of simple pendulum is given by, \(T = 2\pi \sqrt {\frac{l}{g}} \) The time period of a simple pendulum is inversely proportional to the square root of acceleration due to gravity at that point. \(T \propto \frac{1}{{\sqrt g }}\) Therefore, if the acceleration due to gravity increases the time period of the simple pendulum will decrease whereas if the acceleration due to gravity decreases the time. All the simple pendulum increases.

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Calculation of Gravity

Acceleration due to gravity can be measured with the help of a simple experiment, The period \(T\) for a simple pendulum does not depend on the mass or the initial angular displacement but depends only on the length \(L\) of the string and the value of the acceleration due to gravity. Acceleration due to gravity is given by, \(g = \frac{{4{\pi ^2}l}}{{{T^2}}}\) One cam measure the length of the string and observe the time period and the using this formula we can find the acceleration due to gravity

Physical Pendulum

For a simple pendulum, we consider the mass of the string to be negligible as compared to the Bob but for a physical pendulum, the mass of the string need not be negligible in fact any rigid body can act as a physical pendulum.

By writing the torque equation for the rigid body about the fixed point, we get the angular acceleration of the rigid body is directly proportional to the angular displacement by using small-angle approximation. External torque on the system is zero, thus, \({\tau _{{\rm{ext}}}} = 0\)

Writing torque equation about the hinged point we get, \({\tau _0} = mgl{\rm{sin}}\left( \theta  \right) = {I_{\rm{O}}}\alpha\) Solving for \(\alpha ,\) \( \Rightarrow \,\,\,\alpha = \frac{{mgl}}{{{I_{\rm{O}}}}}{\rm{sin}}\left( \theta \right)\) Using small angle approximation, \({\rm{sin}}\left( \theta \right) = \theta \) \( \Rightarrow \,\,\,\alpha = – \frac{{mgl}}{{{I_{\rm{O}}}}}\left( \theta \right)\) Thus the angular frequency is given by, \( \Rightarrow \,\,\,{\omega ^2} = \frac{{mgl}}{{{I_{\rm{O}}}}}\) Time period of a physical pendulum is given by, \(T = 2\pi \sqrt {\frac{{{I_0}}}{{mg{l_{{\rm{cm}}}}}}} \) Where, \({I_0}\) is the moment of inertia about the fixed point trough which the axis passes. \({l_{{\rm{cm}}}}\) is the distance of the centre of mass from the axis point.

Simple Pendulum Application

Simple pendulums are used in clocks as the pendulum has a fixed time period they can be used to keep a track of time. Following are example of a simple pendulum:

Pendulums can be used as metronome.

Pendulums are used to calculate acceleration due to gravity.

Sample Problems on Real Simple Pendulum

1. A simple pendulum is suspended and the bob is subjected to a constant force in the horizontal direction. Find the time period for small oscillation.

Let the magnitude of the force be, \(F.\) Let the angle at equilibrium be, \({\theta _0}\) Let the axes be along the string and perpendicular to the string,

Balancing the forces at equilibrium, \(mg{\rm{sin}}\left( {{\theta _0}} \right) = {F_0}{\rm{cos}}\left( {{\theta _0}} \right)\) \({\rm{tan}}\left( {{\theta _0}} \right) = \frac{{{F_0}}}{{mg}}\) When the pendulum is displaced by some small angle, then,

\(F = {F_0}{\rm{cos}}\left( {\theta + {\theta _0}} \right) – mg{\rm{sin}}\left( {\theta + {\theta _0}} \right)\) \( \Rightarrow F = {F_0}\left[ {{\rm{cos}}\left( {{\theta _0}} \right){\rm{cos}}\left( \theta \right) – {\rm{sin}}\left( {{\theta _0}} \right){\rm{sin}}\left( \theta \right)} \right] – mg\left[ {{\rm{sin}}\left( {{\theta _0}} \right){\rm{cos}}\left( \theta \right) + {\rm{sin}}\left( \theta \right){\rm{cos}}\left( {{\theta _0}} \right)} \right]\) For small oscillation, \({\rm{sin}}\left( \theta \right) = \theta \) \({\rm{cos}}\left( \theta \right) = 1\) \( \Rightarrow \,\,ma = {F_0}{\rm{cos}}\left( {{\theta _0}} \right) – {F_0}{\rm{sin}}\left( {{\theta _0}} \right)\theta – mg{\rm{sin}}\left( {{\theta _0}} \right) – mg{\rm{cos}}\left( {{\theta _0}} \right)\theta \) Using, \(mg{\rm{sin}}\left( {{\theta _0}} \right) = {F_0}\rm{cos}\left( {{\theta _0}} \right)\) We get, \(a = – \frac{{\left[ {{F_0}{\rm{sin}}\left( {{\theta _0}} \right) + mg{\rm{cos}}\left( {{\theta _0}} \right)} \right]}}{m}\theta \) \( \Rightarrow \,\,\,a = – \frac{{\left[ {{F_0}{\rm{sin}}\left( {{\theta _0}} \right) + mg{\rm{cos}}\left( {{\theta _0}} \right)} \right]}}{{ml}}x\) Therefore, the angular velocity is, \({\omega ^2} = \frac{{\left[ {{F_0}{\rm{sin}}\left( {{\theta _0}} \right) + mg{\rm{cos}}\left( {{\theta _0}} \right)} \right]}}{{ml}}\) Putting in the values of \({\rm{sin}}\left( {{\theta _0}} \right)\) and \({\rm{cos}}\left( {{\theta _0}} \right)\) \(\Rightarrow \,\,\,{\omega ^2} = \frac{{\left[ {\frac{{{F_0} \times {F_0}}}{{\sqrt {{{\left( {mg} \right)}^2} + {{\left( {{F_0}} \right)}^2}} }} + \frac{{mg \times mg}}{{\sqrt {{{\left( {mg} \right)}^2} + {{\left( {{F_0}} \right)}^2}} }}} \right]}}{{ml}}\) Thus the time period will be, \(T = \frac{{2\pi }}{\omega }\) \(T = 2\pi \sqrt {\frac{l}{{\sqrt {{g^2} + {{\left( {\frac{{{F_0}}}{m}} \right)}^2}} }}} \)

2. A pendulum is hanging from the roof of a bus moving with a acceleration ‘a’. Find the time period of the pendulum.

Given, The bus is moving with the acceleration ‘\(a\)’. If we apply the concept of inertial and non-inertial frame then, a pseudo force will be applied on the bob,

Let the mass of the bob be, ‘\(m\)’. Therefore, the magnitude of the pseudo force will be, \({F_p} = ma\) The direction of the pseudo force will be in the opposite direction of the acceleration of the bus, Thus if we take the resultant acceleration experienced by the simple pendulum that is the sum of gravitation acceleration \({g_{{\rm{eff}}}} = \sqrt {{g^2} + {a^2}} \) Thus, the time period of the simple pendulum is given by, \(T = 2\pi \sqrt {\frac{l}{{{g_{{\rm{eff}}}}}}} \) Therefore, the time period is, \(T = 2\pi \sqrt {\frac{l}{{\sqrt {{g^2} + {a^2}} }}} \)

A simple pendulum is a mechanical system which consists of a light inextensible string and a small bob of some mass which is made to oscillate about its mean position from left extreme to right extreme. If the displacement of the bob is small as compared to the length of the string or the angle displaced is small then the motion can be considered to be simple harmonic motion. The total energy remains constant throughout the oscillation. The kinetic energy is maximum at the mean position whereas the potential energy is maximum at the extreme positions. The physical pendulum is a mechanical system in which a rigid body is hinged and suspended from a point. For the physical pendulum, we write the torque equation instead of force as it performs angular SHM. The Time period \(T\) for a simple pendulum does not depend on the mass or the initial angular displacement but depends only on the length \(L\) of the string and the value of the acceleration due to gravity. If the effective gravitational acceleration is changed the time period of the oscillation also changes.

FAQs on Simple Pendulum

Q What is the difference between a simple pendulum and a physical pendulum? Ans: Simple pendulum is a mechanical arrangement in which bob is suspended from a point with the help of a massless, inextensible string and performs linear simple harmonic motion for small displacement whereas a physical pendulum is a rigid body hinged from a point and is to oscillate and is performs angular simple harmonic motion for small angular displacement.

Q If a simple pendulum is moving with the acceleration ‘\(g\)’ downwards , what will be the time period of the simple pendulum hanging from its roof? Ans: The effective gravity experienced by the pendulum in this particular case will be zero thus the bob will not perform a simple harmonic motion thus the time period will not be defined as it will not have a periodic motion.

Q Is energy conserved during the oscillation of a simple pendulum? Ans: Yes, in the oscillation of a simple pendulum the total energy remains conserved while the potential and the kinetic energy keep oscillating between maxima and minima with a time period of the half to that of the oscillation of the simple pendulum.

Q What will be the time period of a simple pendulum in outer space? Ans: In outer space, there will be no gravity and thus there will be no restoring force when the pendulum will be displaced thus it will not oscillate and the will be no SHM. Thus, the tie period will not be defined.

Q What type of string should be used in a simple pendulum? Ans: The string in the simple pendulum should be inextensible that is the length of the string should not change with varying force and the mass of the string should be negligible.

We hope this detailed article on Simple Pendulum helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.

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September 23, 2010

How Time Flies: Ultraprecise Clock Rates Vary with Tiny Differences in Speed and Elevation

Newly developed optical clocks are so precise that they register the passage of time differently at elevations of just a few dozen centimeters or velocities of a few meters per second

By John Matson

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If you have ever found yourself cursing a noisy upstairs neighbor, take solace in the fact that he or she is aging faster than you are. Albert Einstein's theory of general relativity predicts that clocks at different gravitational potentials will tick at different rates—a clock at higher elevation will tick faster than will a clock closer to Earth's center. In other words, time passes more quickly in your neighbor's upstairs apartment than it does in your apartment. To complicate matters, the theory of special relativity, which preceded general relativity by a decade, predicts a similar effect for clocks in motion— a stationary clock will tick faster than a moving clock . This is the source of the famous twin paradox: Following a round-trip journey on a spaceship traveling at some exceptionally high velocity, a traveler would return to Earth to find that her twin sibling is now older than she is, because time has passed more slowly on the moving ship than on Earth. Both of these so-called time dilation effects have been verified in a number of experiments throughout the decades, which have traditionally depended on large scales of distance or velocity. In one landmark 1971 test Joseph Hafele of Washington University in Saint Louis and Richard Keating of the U.S. Naval Observatory flew cesium atomic clocks around the world on commercial jet flights, then compared the clocks with reference clocks on the ground to find that they had diverged, as predicted by relativity . But even at the speed and altitude of jet aircraft, the effects of relativistic time dilation are tiny—in the Hafele–Keating experiment the atomic clocks differed after their journeys by just tens to hundreds of nanoseconds. Thanks to improved timekeeping, similar demonstrations can now take place at more mundane scales in the laboratory. In a series of experiments described in the September 24 issue of Science , researchers at the National Institute of Standards and Technology (NIST) in Boulder, Colo., registered differences in the passage of time between two high-precision optical atomic clocks when one was elevated by just a third of a meter or when one was set in motion at speeds of less than 10 meters per second. Again, the effects are minuscule: It would take the elevated clock hundreds of millions of years to log one more second than its counterpart, and a clock moving a few meters per second would need to run about as long to lag one second behind its stationary counterpart. But the development of optical clocks based on aluminum ions, which can keep time to within one second in roughly 3.7 billion years, allows researchers to expose those diminutive relativistic effects. "People usually think of it as negligible, but for us it is not," says lead study author James Chin-wen Chou , a postdoctoral research associate at NIST. "We can definitely see it." The NIST group's optical clocks use lasers to probe the quantum state of aluminum ions held in radio-frequency traps. When the laser's frequency is just right, it resonates with a transition between quantum states in the aluminum ion whose frequency is constant in time. By constantly tuning the laser to drive that aluminum transition, an interaction that only occurs in a tiny window near 1.121 petahertz (1.121 quadrillion cycles per second), the laser's frequency can be stabilized to an exquisitely sensitive degree, allowing it to act as the clock's pendulum. "If we anchor the frequency of the oscillator—in our case, laser light—to the unchanging, stable optical transition in aluminum, the laser oscillation can serve as the tick of the clock," Chou explains. To put the sensitivity of the optical clocks in perspective, Chou notes that the two timekeepers in the study differed after a height change of a mere step on a staircase—never mind the entire floor separating you from your noisy neighbor—or with just a few meters per second of motion. "If you push your daughter on a swing, it's about that speed," he says. In the past, such relativistic experiments have involved either massive scales of distance or velocity, or else oscillations so fast that their ticks cannot be reliably counted for timing purposes, says Holger Müller , an atomic physicist at the University of California, Berkeley. "It's an enormous achievement that you can build optical clocks so good that you can now see relativity in the lab," he says. Müller has used atom interferometry to make precision measurements of relativistic effects, measurements that rely not on counting individual oscillations but on tracking the interference between two waves. (The frequencies of such waves, which oscillate tens of billions of times faster than the petahertz laser in an aluminum clock, are simply too high to monitor and count.) It is a process akin to striking two tuning forks to listen to the pulsations of their interference, without actually measuring how many times each fork vibrates. In that sense atom interferometers are pendulums without clockwork, so although they can make physical measurements with great precision, they cannot be used to keep time. "The new work operates on familiar scales of distance and velocity, with clocks that can be used for universal timing applications," Müller says. "They see the effects of general and special relativity, and that makes relativity something you can kind of see and touch."

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Long-Baseline Neutrino Experiments March On

• Institute of Research into the Fundamental Laws of the Universe (IRFU), French Atomic Energy Commission (CEA), Saclay, France

In 1998, researchers discovered that neutrinos can change their “flavor” as they travel. This behavior is only possible if neutrinos have a mass—contrary to the initial assumption of the standard model of particle physics. The discovery of this beyond-standard-model behavior, recognized by the 2015 Nobel Prize in Physics, drove intense efforts to characterize neutrino oscillations through increasingly accurate experiments. One such effort, the NOvA experiment at Fermilab, now reports the analysis of oscillation data collected between 2014 and 2020 [ 1 ], delivering some of the most accurate estimates to date of parameters describing neutrino oscillations and providing important hints on two important aspects of neutrino physics—the ordering of neutrino masses and the degree of charge-parity (CP) violation. The results bode well for the next generation of “long-baseline” experiments, which will dramatically boost our ability to probe elusive aspects of neutrino physics.

When neutrinos of a given type, or flavor, travel over some distance, they can switch their flavor with a probability depending on distance and on neutrino energy. This oscillation can be explained by assuming that there are three neutrino mass eigenstates that mix to form three flavor eigenstates (electron, muon, and tau) among which oscillations occur. Such behavior is parametrized (that is, mathematically described by a limited set of measurable numbers) by the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix. As often occurs in physics, precision measurements of a phenomenological parametrization can deliver hints to new physics—which could mean developing a simpler model connected to a smaller set of parameters or even discovering a more fundamental theory, solely based on symmetries, that describes observations.

Today’s experiments aim to tackle, in particular, two crucial open questions. First, are neutrinos ordered in mass in a similar way (“normal ordering”) as their charged-lepton partners, the well-known electron, muon, and tau particles? A naive analogy would suggest that this is the case—but finding an “inverted ordering” would be an exciting result that could guide theoretical developments. Second, do neutrinos oscillate in the same way as their antiparticles (antineutrinos), that is, do they obey CP symmetry (Fig. 1 )? If not, we would establish, for the first time, CP violation by leptons (the particle sector that includes neutrinos, electrons, muons, and taus). CP violation is at the heart of one of physics’ greatest puzzles—matter’s dominance over antimatter in the Universe. Understanding CP violation in different particle sectors, including leptons, could help in solving this puzzle.

The discovery of neutrino oscillations was enabled by two natural sources of neutrinos: cosmic rays hitting Earth’s atmosphere, and nuclear reactions in the Sun. Today, artificial neutrino sources, such as particle accelerators, allow researchers to better control the flavor and energy of the produced neutrinos and the distance, or “baseline,” over which these particles travel before they are detected. Particle accelerators can work in neutrino-beam and antineutrino-beam modes, producing separate fluxes of neutrinos and antineutrinos, which is crucial for CP-violation searches. Presently, two accelerator experiments have long enough baselines to observe PMNS neutrino oscillations: T2K in Japan and NOvA in the US, with baselines of 295 and 810 km, respectively.

In 2020 the two collaborations announced results that indicated an intriguing, yet mild, tension [ 2 , 3 ]. Both experiments slightly favored normal ordering over inverted ordering, although NOvA, by virtue of its longer baseline, has a much more pronounced sensitivity to mass ordering. The T2K experiment suggested that neutrinos oscillate faster than antineutrinos—implying a large CP violation. The degree of CP violation extracted from NOvA’s results, however, depended on mass ordering. For normal ordering, NOvA favored a small CP violation, whereas for inverted ordering, NOvA’s results would be compatible with T2K’s. Statistical fluctuations are the most economical explanation for these differences, but the tension is an opportunity for a deep investigation of the systematic uncertainties affecting these measurements. More exotic explanations for the tension, including “nonstandard” interactions of neutrinos, have been also proposed.

NOvA’s new report [ 1 ] offers a detailed description of the results announced in 2020. With respect to the previous analysis published by NOvA in 2019 [ 4 ], the new one includes about 50% more data in neutrino-beam mode and the reanalysis of all data taken since 2014. The reanalysis is further optimized to exploit the fact that NOvA’s near and far detectors are based on the same technology, using a procedure that partly cancels out systematic uncertainties. NOvA mostly produces muon neutrinos or antineutrinos and uses as main observables the number and energy of muon neutrinos and antineutrinos that survive the trip to the far detector and the number and energy of electron neutrinos that appear at the far detector. From these measured observables, the analysis extracts estimates of oscillation parameters, of mass ordering, and of the degree of CP violation.

Since the 2020 announcement, a number of researchers have already performed “joint fits” to the sets of data coming from NOvA, T2K, and other experiments (including those using neutrinos produced by nuclear reactors, by the Sun, and by cosmic rays) [ 5 – 7 ]. These joint fits favor normal ordering, with a degree of CP violation lying between NOvA’s and T2K’s. The preference for normal ordering is highly influenced by data from Super-Kamiokande—an observatory in Japan that measures cosmic-ray-produced neutrinos—which is sensitive to mass ordering. When T2K and NOvA results are included in the fits, such preference diminishes because inverted ordering would release the tension between those experiments seen for normal ordering. Clearly, there is more work to be done. Those joint fits, however, cannot account for correlations of the systematic uncertainties between NOvA and T2K. Fortunately, the two experiments are cooperating to produce a new joint fit that will clarify the possible impact of such correlations when combining their measurements.

So, what does the future hold in store? A new generation of long-baseline experiments under construction, such as Hyper-Kamiokande in Japan and the Deep Underground Neutrino Experiment (DUNE) in the US, will boost the available statistics by more than a factor of 20. At that point, an unprecedented control over the systematic uncertainties will be needed. The most complex of those uncertainties—associated with the modeling of neutrino production and of neutrino-nucleus interactions—touch on deep nuclear-physics problems that require a close collaboration with the nuclear-physics community. The statistics boost is likely to allow researchers to make some easy progress: establishing the mass hierarchy and the degree of CP violation. But with the flurry of data becoming available in the longer term, we may need to look at neutrino oscillation with a more open mind, possibly relaxing some of the restrictive assumptions of the current paradigm, such as a unitary PMNS matrix and a minimal scenario involving only three neutrino flavors and only standard interactions.

To control systematic uncertainties and allow for a more model-independent interpretation of the data, the combination of complementary experiments with different baselines and neutrino energies will be crucial. T2K and NOvA are showing how powerful these synergies can be. A guiding example for neutrino searches may come from the most celebrated success of particle physics—the discovery of the Higgs boson. Such success was built on multiple generations of experiments that constantly improved their performance and refined the fundamental understanding of the electroweak sector, as well as on the combination of the two major Higgs-searching experiments—ATLAS and CMS.

• M. A. Acero et al. , “Improved measurement of neutrino oscillation parameters by the NOvA experiment,” Phys. Rev. D 106 , 032004 (2022) .
• A. Himmel (NOvA Collaboration), “New oscillation results from the NOvA experiment,” Neutrino 2020 (2020) , Zenodo.
• P. Dunne (T2K Collaboration), “Latest neutrino oscillation results from T2K,” Neutrino 2020 (2020) , Zenodo.
• M. A. Acero et al. (NOvA Collaboration), “First measurement of neutrino oscillation parameters using neutrinos and antineutrinos by NOvA,” Phys. Rev. Lett. 123 , 151803 (2019) .
• P. F. de Salas et al. , “2020 global reassessment of the neutrino oscillation picture,” J. High Energ. Phys. 2021 , 71 (2021) .
• F. Capozzi et al. , “Unfinished fabric of the three neutrino paradigm,” Phys. Rev. D 104 , 083031 (2021) .
• I. Esteban et al. , “The fate of hints: Updated global analysis of three-flavor neutrino oscillations,” J. High Energ. Phys. 2020 , 178 (2020) .

About the Author

Sara Bolognesi is a staff physicist at the Institute of Research into the Fundamental Laws of the Universe (IRFU) of the French Atomic Energy Commission (CEA), Saclay. She received her Ph.D. in 2008 from the University of Turin, Italy. She did postdoctoral work at CERN in Switzerland and Johns Hopkins University and Fermilab, both in the US. She worked on the CMS experiment at the Large Hadron Collider where she contributed to detector commissioning and to the Higgs discovery. She then moved to work on neutrino physics with the T2K experiment in 2013. Today, she is the analysis coordinator for T2K and the leader of the IRFU group working on neutrinos from accelerators. Bolognesi is a recipient of the Thibaud Prize of the Academy of Sciences, Letters, and Arts of Lyon and of the Emmy Noether Award from the European Physical Society.

Improved measurement of neutrino oscillation parameters by the NOvA experiment

M. A. Acero et al. (The NOvA Collaboration)

Phys. Rev. D 106 , 032004 (2022)

Published August 3, 2022

Subject Areas

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The Time Dilation Experiment: How Physicists Prove Its Real

As a team of physicists, we are fascinated by the concept of time dilation. It is a fundamental aspect of Einstein's Theory of Relativity that describes how time can appear to pass differently for two observers in different frames of reference. This theory has been proven experimentally time and time again, and today we want to take you through some of the most compelling experiments that have been conducted to demonstrate this phenomenon.

The first thing we need to understand is what time dilation actually means. In simple terms, it refers to the fact that time appears to move slower for an observer who is moving relative to another observer who is stationary. This may sound counterintuitive, but it has been demonstrated repeatedly through carefully designed experiments. These experiments not only help us better understand the nature of our universe but also have practical implications in fields such as GPS technology and space travel. So let's dive into the exciting world of physics and explore some fascinating examples of how physicists prove that time dilation is real!

Understanding Time Dilation Theory

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Understanding the mind-bending theory of time dilation is essential for grasping the intricacies of Einstein's theory of relativity. In simple terms, time dilation can be defined as the difference in elapsed time between two events that occur at different distances from a gravitational mass or relative to each other's motion. This means that time passes slower for an object in motion or near a massive object than it does for an observer who is stationary and far away.

To understand this concept better, let's take an example. Imagine two synchronized clocks placed at different altitudes - one on top of Mount Everest and another at sea level. According to the theory of general relativity, because gravity is weaker at higher altitudes, the clock on Mount Everest would tick faster than the one at sea level. This phenomenon can be explained mathematically using equations such as Lorentz transformations and special relativity formulas.

With this understanding of time dilation, we can now delve into the concept of time dilation experiment without missing any crucial details.

](/blog/time-travel-theories/time-dilation/time-dilation-experiment-physicists-prove-real)As we delve deeper into the concept of measuring time in different ways, a mind-bending realization starts to take shape. The theory of relativity suggests that time is not constant and can be influenced by various factors, such as gravity and motion. To prove this theory, physicists have conducted numerous experiments over the years using advanced measurement techniques and observational evidence.

To further illustrate the concept of time dilation, here are some key points to consider:

• According to the theory of relativity, time passes more slowly in strong gravitational fields or at high velocities.
• This means that if two individuals were traveling at different speeds or in different gravitational fields, they would experience time differently.
• The first experimental evidence for time dilation came from the famous Hafele-Keating experiment in 1971, which involved atomic clocks being flown around the world on commercial airliners.

With these ideas in mind, let us explore how physicists were able to conduct their first time dilation experiment.

You will delve into the first demonstration of time's non-constant nature through an experiment using advanced measurement techniques and observational evidence. The first time dilation experiment was conducted by two physicists, Joseph Hafele and Richard Keating, in 1971. They flew atomic clocks on separate commercial airplanes that traveled around the world in opposite directions. This experimental setup allowed them to compare the elapsed time of one clock with respect to another.

The data collection process involved comparing the readings of the clocks after they returned from their journeys. The results showed that the clock traveling westward experienced a slower passage of time than the stationary clock on Earth, whereas the clock flying eastward experienced a faster passage of time than its counterpart on Earth. This finding provided strong evidence for Einstein's theory of relativity and proved that time dilation is not just a theoretical concept but a real phenomenon that occurs in our universe.

This groundbreaking experiment paved the way for further research into understanding how gravity affects space-time and led to more recent time dilation experiments exploring new frontiers such as black holes and neutron stars.

In recent years, there have been several groundbreaking experiments that further prove the existence of time dilation. One such experiment involved atomic clocks, which are incredibly precise timekeeping devices. By measuring the differences in time between two identical atomic clocks (one stationary and one in motion), scientists were able to observe time dilation effects predicted by Einstein's theory of relativity.

Another experiment involved observing gravitational time dilation, which occurs when an object is located near a massive body causing it to experience slower time than an observer farther away from the massive body. Scientists observed this effect by using extremely sensitive atomic clocks placed at different heights above sea level.

The results and analysis of these experiments provide even more evidence for the reality of time dilation and its importance in our understanding of physics.

You'll feel the ticking of an atomic clock in your bones as you imagine the precision and accuracy required for this experiment. Atomic clocks are the standard for measuring time with extreme accuracy, relying on the natural vibrations of cesium atoms to keep incredibly precise time. The recent atomic clock experiment conducted by physicists tested whether or not time dilation occurs at different altitudes above Earth's surface.

The test involved comparing two identical atomic clocks: one kept on the ground and another taken up to a high altitude via airplane. The results confirmed that time dilation does indeed occur, with the higher altitude clock running slightly faster than its grounded counterpart due to gravitational differences. This level of atomic clock accuracy is essential for measuring even the smallest differences in time dilation, providing crucial data for theories like Einstein's theory of relativity.

Now, let's move on to the next step where we explore how physicists conduct experiments that prove gravitational time dilation is real.

Get ready to feel the thrill of discovery as we delve into the fascinating world of gravitational time differences and how they can be measured with incredible precision. The gravitational time dilation experiment involves measuring the difference in time between two clocks placed at different altitudes in a gravitational field. As Einstein's theory of general relativity predicted, time moves slower closer to a massive object due to the curvature of space-time caused by gravity.

Experimental evidence for this effect was first observed in 1962 when atomic clocks on board airplanes flew around the Earth and were found to be out of sync with identical clocks on the ground. More recent experiments have used highly precise atomic clocks flown on airplanes or launched into space satellites to measure these effects even more accurately. These experiments have also been able to detect other factors that can affect time dilation, such as changes in velocity and gravitational waves. With this technology, physicists are able to confirm that general relativity is indeed an accurate description of our universe.

As we move onto discussing results and analysis, it's important to note that these experiments have not only provided evidence for Einstein's theory but also opened up new avenues for research into fundamental physics, including investigations into dark matter and quantum gravity.

Now we can finally see the fascinating and groundbreaking results that confirm Einstein's theory of general relativity. The gravitational time dilation experiment has provided evidence that time slows down in stronger gravitational fields, which is consistent with the predictions made by the theory. By using precision measurement techniques to compare atomic clocks at different altitudes, scientists have demonstrated that time passes more slowly closer to massive objects.

The results obtained from this experiment are statistically significant and provide strong support for Einstein's theory. They indicate that gravity affects not only space but also time, which is a fundamental concept in physics. These findings have important implications for our understanding of the universe and its behavior. As we move on to discussing the implications of time dilation, we must keep in mind how crucial these experimental results are for advancing our knowledge of physics.

So now that we understand the basics of time dilation and how it has been experimentally proven, let's look at some of its implications. First, there are practical applications for space travel: as objects near the speed of light experience less time than those at rest, astronauts on long space missions could age slower than their counterparts on Earth. Secondly, time dilation has theoretical implications for our understanding of the nature of time itself and its relationship to space. Finally, continued research and development in this area could lead to new technologies and a deeper understanding of fundamental physics.

You'll be fascinated to learn that space travel could become more efficient and faster with the use of time dilation, as demonstrated by the fictional spacecraft in the movie Interstellar. The concept behind this is simple: if astronauts travel at a speed close to the speed of light, their time will slow down relative to those on Earth. This means that they can effectively age slower than their counterparts back home, allowing them to spend more time exploring and less time aging.

This has huge implications for astronaut travel, as it means that we can potentially send humans on long-duration missions without worrying about the effects of prolonged exposure to zero gravity. Furthermore, it also opens up possibilities for interstellar travel and even time travel (in theory). Of course, there are still many technical challenges that need to be overcome before we can realize these dreams, but it's an exciting prospect nonetheless. With all of this in mind, let's delve deeper into the theoretical implications of time dilation.

We can hardly contain our excitement as we explore the mind-boggling theoretical implications of time slowing down at high speeds. Philosophical considerations arise when we ponder how this phenomenon challenges our understanding of the nature of time itself. Our traditional view of time as an absolute and constant entity is shattered by the reality that it can warp and distort depending on relative motion.

The practical implications are equally fascinating. Time dilation has been observed in experiments involving atomic clocks, which have shown that even fractions of a second can make a significant difference over long distances or high velocities. This has important implications for GPS systems, where precise timing is critical for accurate location tracking. As we continue to unravel the mysteries of time dilation, future applications in fields such as space travel and telecommunications may become possible. But first, more research and development is needed to fully harness this incredible phenomenon.

You're about to discover the exciting possibilities that lie ahead in the field of researching and developing new technologies that can harness the incredible effects of time distortion at high speeds. With the confirmation of time dilation through experiments, scientists are now exploring ways to apply this phenomenon in innovative timekeeping devices and space travel. One potential application is using atomic clocks on spacecraft to accurately measure time in space, where the effects of gravity and velocity can distort time.

Technological advancements in quantum mechanics and nanotechnology are also paving the way for more precise measurements of time dilation. Researchers are experimenting with using quantum entanglement to create ultra-precise clocks that could be used for navigation or even detecting gravitational waves. As we continue to uncover more about this fascinating aspect of physics, it's clear that there are countless possibilities for future research and development in this field.

When discussing time dilation theory, it's impossible not to mention Einstein's contributions to the field of physics. His theory of relativity revolutionized our understanding of space and time, showing that they are intertwined and not absolute. Time perception is a crucial aspect of this theory, as it suggests that time can appear differently depending on one's frame of reference. This idea has been tested and proven in various experiments, including the famous Hafele-Keating experiment where atomic clocks were flown around the world to measure differences in elapsed time due to changes in velocity and gravity. Overall, Einstein's work on relativity paved the way for further exploration into the nature of time and how it relates to our physical universe.

When it comes to performing time dilation experiments, there are certainly limitations and potential drawbacks to consider. One major limitation is the accuracy of the experiment itself. In order to measure time dilation accurately, physicists must use incredibly precise instruments and methods. Even small errors in measurement could lead to inaccurate results, which could have serious implications for our understanding of the universe. Another potential drawback is that time dilation experiments can be incredibly complex and difficult to carry out. They require a great deal of planning, resources, and expertise, which may not always be available. Despite these challenges, however, time dilation experiments remain an important tool for physicists seeking to better understand the nature of time and space.

When it comes to practical implications of time dilation, physicists have developed experimental methods that help account for its effects. For instance, GPS systems rely on precise timing to determine a user's location. However, the satellites that send signals to GPS devices are in motion relative to the Earth and therefore experience time dilation. To ensure accurate timing, scientists must adjust the clocks on the satellites based on calculations of their velocity and altitude. By doing so, they can correct for the effects of time dilation and provide users with reliable location data. Overall, while time dilation can pose challenges in certain applications, physicists have found ways to mitigate its impact through careful experimentation and analysis.

Everyday examples of time dilation can be observed in our daily lives. One example is the aging process, where time appears to pass more quickly for those who are moving at higher speeds relative to a stationary observer. Experimental methods have also been used to prove the existence of time dilation, such as high-speed particle accelerators and spacecraft traveling at high velocities. These experiments have shown that time dilation is not just a theoretical concept, but a real phenomenon that occurs in extreme conditions as well as everyday situations.

Future implications of time dilation theory are vast and exciting. Technological advancements in the field will allow for more precise measurements, leading to a deeper understanding of the universe's fundamental workings. To put this into perspective, consider that the world's most accurate atomic clock loses only one second every 15 billion years due to time dilation effects. This level of precision is necessary for research in areas such as space exploration, satellite communication, and GPS technology. As we continue to push the limits of our understanding of time and space, time dilation theory will undoubtedly play a crucial role in shaping our future discoveries and innovations.

So, there you have it – time dilation is not just a theory, but a proven fact. Through various experiments conducted over the years, physicists have demonstrated that time really does slow down when an object moves at high speeds or experiences intense gravitational forces.

But what does this mean for us? Well, it has implications for everything from our GPS systems (which rely on precise timing) to our understanding of the universe itself. It's mind-boggling to think about how much we've learned through these experiments and how much more we still have yet to discover. The possibilities are endless and truly exciting.

In conclusion, time dilation is one of those concepts that can seem too abstract and outlandish to be believed at first glance. But thanks to the hard work and ingenuity of countless scientists over the years, we now know that it's real – a verified phenomenon that shapes our world in ways we're only beginning to understand. It's proof that sometimes even the wildest theories can turn out to be true – a testament to human curiosity and perseverance if ever there was one.

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September 17, 2024

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Graphite oxidation experiments reveal new type of oscillating chemical reaction

by Umea University

A reaction that puzzled scientists for 50 years has now been explained by researchers at Umeå University. Rapid structural snapshots captured how graphite transforms into graphite oxide during electrochemical oxidation, revealing intermediate structures that appear and disappear over time. The researchers describe this as a new type of oscillating reaction.

The study has been published in the journal Angewandte Chemie .

Oscillating chemical reactions are fascinating to watch and important for developing an understanding of how complex systems work, both in chemistry and in nature. Classical visual examples of such reactions show how the colors of a solution change back and forth, cycling through different states and producing a final product after each cycle.

"It has been known for 50 years that some voltage oscillations spontaneously occur when a charge is applied to a graphite electrode immersed in sulfuric acid solution. The end product of this reaction is graphite oxide , a material consisting of layers of graphene oxide. However, what happens to the structure of the material during the reaction at every oscillation cycle had remained a complete mystery," says Alexandr Talyzin, Professor in the Department of Physics at Umeå University.

Thanks to new synchrotron methods, researchers can record X-ray diffraction scans in a matter of a few seconds, providing snapshots of the material's structure changes during oxidation. Surprisingly, the experiments revealed an intermediate phase with a specific structure that appears at one part of the cycle, disappears in the next stage and then reappears, repeating the cycle.

"Soon we realized that we had observed a new—to the best of our knowledge—type of oscillating reaction. What began as a detailed study of a particular chemical reaction suddenly appeared to be a lot more interesting from the point of view of fundamental chemistry. Bartosz Gurzeda, the first author of the study, also recorded a beautiful video showing periodic changes in the appearance of a sample every few minutes," says Talyzin.

Oscillation reactions are happening inside all living beings but were once considered impossible in inorganic chemistry. This discovery expands our knowledge of chemical kinetics and reaction mechanisms and could lead to the development of new theories and models in chemistry.

The first theory explaining oscillating reactions earned Ilya Prigogine the Nobel Prize in 1977 and became a fundamental part of non-equilibrium thermodynamics, showing how order can emerge from chaos.

"We hope that new theories will be developed to explain this new type of oscillating reaction, which may lead to the discovery of new similar examples," says Talyzin.

Journal information: Angewandte Chemie

Provided by Umea University

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MK-ULTRA: Ottawa, health centre seek to dismiss Montreal brainwashing lawsuit

Family members of patients allegedly brainwashed decades ago at a Montreal psychiatric hospital are afraid they're running out of time to get compensation because the federal government and the McGill University Health Centre have filed motions to dismiss their lawsuit.

Glenn Landry's mother, Catherine Elizabeth Harter, was among the hundreds of people to receive experimental treatments under the MK-ULTRA program, funded by the Canadian government and the CIA between the 1940s and 1960s at Montreal's Allan Memorial Institute, which was affiliated with McGill University.

Landry was born after his mother's 1959 stay in the hospital, and had to be raised by a foster family because she couldn't care for him.

While he says early traumas she experienced before seeking treatment undoubtedly played a role in her mental health issues, he believes the shock treatments and drug therapy she received during her months-long stay under the care of Dr. Donald Ewen Cameron and his colleagues robbed him of a relationship with her.

"She was no longer the person that she would have been, because there was no way that I could ever ask her about any kind of memories," he said of his mother, who he saw about once a year until her death in the 1980s.

"She spent time with me because I was her son, but there was nothing about herself as a person that I can glean. It was not there."

Landry represents one of about 60 families participating in a lawsuit against the Canadian government, the McGill University Health Centre and the Royal Victoria Hospital over the MK-ULTRA program. The plaintiffs allege their family members were subjected to psychiatric experimentation that included powerful drugs, repeated audio messages, induced comas and shock treatment that reduced them in some cases to a childlike state.

Lawyer Alan Stein, who represents the group, said he had been hopeful the government and hospitals would agree to start talks around compensation for his clients — many of whom are elderly. Instead, the opposing parties filed motions in Quebec Superior Court last week to dismiss, arguing the lawsuit is "unfounded in law and constitutes an abuse of procedure."

The government and hospitals argue the claims are prescribed — that they should have been filed years or even decades ago when the facts surrounding the case first came to light.

"In addition to being prescribed, the originating application is an abuse of process in that it seeks to re-litigate determinative questions of fact and law that the courts of Quebec adjudicated over two decades ago," one of the motions read.

In an email, a spokesperson for Canada's Department of Justice says the government "acknowledges the hurt and pain inflicted on those impacted by these historical treatments," but believes the claims are unfounded.

The department said a 1986 report into Cameron's work found that the Canadian government did not hold legal liability or moral responsibility for the treatments but nevertheless decided to provide victims with assistance in the 1990s for "humanitarian reasons." The McGill University Health Centre declined to comment.

Stein, in a phone interview, says the motion to dismiss is a delaying tactic from government lawyers. "They feel that my clients will not proceed further, that they'll lose confidence and just not agree to continue further with the proceedings," he said.

He says his clients should still have the right to sue because they didn't know earlier that it was an option available to them. And while some victims were compensated, the money for the most part did not extend to family members, he added.

The lawsuit is asking for close to $1 million per family, for what Stein calls a "total miscarriage of justice."

Landry compares the victims' long legal ordeal to the wait Japanese Canadian survivors of Second World War internment camps faced before receiving justice, and he says MK-ULTRA victims also want an apology.

Because another group of Cameron’s alleged victims, and a different lawyer, had previously filed a class-action request, Stein chose instead to file a direct action, which allows plaintiffs to be mandated by others in similar circumstances to sue on their behalf. Quebec Superior Court set the stage for a trial in 2022 when it rejected an application by the government and the hospitals to partially dismiss the lawsuit, but the process was dragged out by an appeal, which also failed.

The proposed class-action lawsuit representing the other victims had tried to include the United States government as a defendant, but Quebec's Court of Appeal ruled earlier this year that the U.S. state cannot be sued in Canada for its alleged role in the experiments; the Supreme Court of Canada refused to review the case.

While the two lawsuits are separate, Stein believes a victory by the government and hospitals in his lawsuit would make it very hard for the other effort to move forward since it would likely be targeted with a similar motion.

One of the two named plaintiffs in Stein's suit has already dropped out. Marilyn Rappaport said in an interview that she withdrew after her husband died. That devastating loss, combined with her ongoing need to support her siblings who were victims of the experiments, made it too hard to contemplate the prospect of reliving her terrible childhood memories in court, she said.

Rappaport says her once beautiful and artistic sister Evelyn has experienced what she describes as a “living death” in the decades since she went to the hospital for treatments including being put to sleep for “months at a time” and subjected to audio messages on repeat. Now in her 80s, her sister is institutionalized and her memory is "totally gone," Rappaport says.

While she's no longer part of the lawsuit, Rappaport is still hoping for a victory and upset that the government is still fighting.

"I cannot understand why it's taking so long," she said.

This report by The Canadian Press was first published Sept. 17, 2024.

This is a corrected story. A previous version said McGill University filed a motion to dismiss the lawsuit. In fact, it was the McGill University Health Centre. 

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