Why does amplitude not affect period

You can say it's because average speed in the RMS sense scales in the same way as displacement does: double the amplitude, and the RMS speed will also double. To first-order approximation at least. Why would that be? Well, it's because average acceleration also scales proportionally, as that simply depends on the force. It's the particular feature of the harmonic oscillator that force depends linearly on displacement. One possible approach to explain why the period does increase with initial angular starting off point is to imagine a pendulum where the string is made of taut wire.

In this case the pendulum is in exact equilibrium and you may then say that the period is infinite. Now, you'd expect the relationship between the period and the starting angle to be monotonic, and since it starts off small for small angles, if the period increases from something small to infinite, at in-between starting angles you'd expect the period to get larger as the starting angle increases.

For small enough angles, this monotonic function presumably is flat, meaning that period is roughly independent of initial starting angle. The larger the swing, the more vertical is the angle at which the pendulum bob starts falling at, hence the faster it accelerates at the start, and the increase in speed exactly balances the longer swing length. Just read Enn's answer in more detail, and my answer is, more or less, a more intuitive presentation of his.

The best answer is to combine his and mine: larger acceleration at start due to increased angle, and larger fall distance, hence faster movement. I wrote this answer as a response to this question but as it was marked as a duplicate I add to the answers here.

The most important thing is that the acceleration and hence the force is proportional to the displacement from a fixed point. This analysis shows that for the amplitude to be the common factor in successive displacements there must be a linear relationship between the acceleration and the displacement. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Intuition - why does the period not depend on the amplitude in a pendulum? Ask Question. Asked 4 years, 3 months ago. Active 4 years, 1 month ago. Viewed 21k times. Improve this question. Noam Chai Noam Chai 1 1 gold badge 4 4 silver badges 15 15 bronze badges.

The only intuitive thing you can say is that the change is too small to observe. Add a comment. Active Oldest Votes.

Improve this answer. JMac JMac When the angle is small the periodic bevaivour appears linear and approximately is , and this relationship only applies when it is linear. Since it is only ever approximately linear, they are only approximately the same period. Suppose you pluck a banjo string. You hear a single note that starts out loud and slowly quiets over time.

Describe what happens to the sound waves in terms of period, frequency and amplitude as the sound decreases in volume. A babysitter is pushing a child on a swing. At the point where the swing reaches x , where would the corresponding point on a wave of this motion be located? The point on the wave would either be at the very top or the very bottom of the curve.

A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring. Figure 6. What is the new period of oscillation when a second skydiver, whose mass is Figure 7. The oscillations of one skydiver are about to be affected by a second skydiver. Army, www. Skip to main content. Oscillatory Motion and Waves.

Search for:. Explain the link between simple harmonic motion and waves. Note that neither T nor f has any dependence on amplitude. Example 1. Calculate the Frequency and Period of Oscillations: Bad Shock Absorbers in a Car If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping See Figure 2.

Check Your Understanding Part 1 Suppose you pluck a banjo string. Solution Frequency and period remain essentially unchanged.

Only amplitude decreases as volume decreases. Part 2 A babysitter is pushing a child on a swing. Solution x is the maximum deformation, which corresponds to the amplitude of the wave.

Click to run the simulation. Conceptual Questions What conditions must be met to produce simple harmonic motion? Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material. As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty?

Explain your answer. Ask students the following questions in order to get a feel for their current knowledge and perceptions of pendulums. Answers to these questions are provided for you, but don't expect or lead students to these answers yet.

At this point, simply gather and keep a good record of students' current ideas; students will have a chance to refine these after the website exploration that follows. Many students believe that changing any of the variables string length, mass, or where we release the pendulum will change the frequency of the pendulum.

Give them a chance to debate and discuss their answers before continuing. After students have explored these sites, review with them their list of answers to the initial questions about pendulums, revising it with the current information based on the students' exploration of the websites. As you review their answers to the question, "What variables affect the rate of a pendulum's swing? Begin this part of the lesson by telling students that they will explore websites to learn more about how pendulums help us learn about gravitational forces.

In the second part of the lesson, students will work in groups to construct their own pendulums and test what they have observed on the websites. Have students run the demonstration called the Pendulum Lab. With this lab, students can play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing.

Make sure they understand how to run the experiment by telling them the following:. With this demonstration, you can observe how one or two pendulums suspended on rigid strings behave. You can click on the bob the object at the end of the string and drag the pendulum to its starting position.

Also, you can adjust the length and mass of the pendulum by adjusting the the controls in the green box on the right side of the page. The pendulum can be brought to its new starting position by clicking on the "Reset" button. You also can measure the period by choosing the "photogate timer" option in the green box.

Explain the features of this demonstration to your students:. In this demonstration, you can vary the length of the pendulum and the acceleration of gravity by entering numerical values or by moving the slide bar. Also, you can click on the bob and drag the pendulum to its starting position.

This demonstration allows you to measure the period of oscillation of a pendulum. Students can also measure the frequency of a pendulum, or the number of back-and-forth swings it makes in a certain length of time.

By counting the number of back-and-forth swings that occur in 30 seconds, students can measure the frequency directly. Ask students:. At this point, students should understand that gravitational forces cause the pendulum to move. They should also understand that changing the length of the bob or changing the starting point will affect the distance the pendulum falls; and therefore, affect its period and frequency. Divide students in cooperative groups of two or three to work together to complete this activity.

As outlined, students will first make predictions and then construct and test controlled-falling systems, or pendulums, using the materials listed and following the directions on the worksheet. This controlled-falling system is a weight bob suspended by a string from a fixed point so that it can swing freely under the influence of gravity. If the bob is pushed or pulled sideways, it can't move just horizontally, but has to move on the circle whose radius is the length of the supporting string.

It has to move upward from where it started as well as sideways. If the bob is now let go, it falls because gravity is pulling it back down. It can't fall straight down, but has to follow the circular path defined by its support. This is "controlled falling": the path is always the same, it can be reproduced time after time, and variations in the set-up can be used to test their effect on the falling behavior.

Note: Make sure that the groups understand that by changing the value of only one variable at a time mass, starting angle, or length , they can determine the effect that it has on the rate of the pendulum's swing.

Also, students should be sure the measurements with all the variables are reproducible, so they are confident about and convinced by their answer. After students have completed the experiments, discuss their original predictions on the activity sheet and compare them with their conclusions based on the data and the results of the tests.

Older students should probably learn how the downward force of gravity on the bob is split into a component tangential to the circle on which it moves and a component perpendicular to the tangent coincident with the line made by the supporting string and directed away from the support.

The tangential force moves the bob along the arc and the perpendicular force is exactly balanced by the taut string. Now, based on these observations, determine what conclusions students can make about the nature of gravity. Students should conclude that gravitational force acting upon an object changes its speed or direction of motion, or both. If the force acts toward a single center, the object's path may curve into an orbit around the center.