How Does Amplitude Influence the Oscillation Period of a Cantilever?

[singh246]

1) Does the amplitude of a cantilever affect the time period of each oscillation when the experiment is set up like http://www.practicalphysics.org/go/Experiment_430.html

2) Please explain your answer.

3) The equation I am using is T= 2pi* sqrt ((4ML^3)/(Ebd^3)). Now this equation works out the time period of the vibrations, but if the time period is changing what does this equation work out?

4) I am planning to set up the experiment as shown in the link, but how would I set the cantilever into motion in order to make the formula work. Do I just let the mass at the end of the cantilever drop?

Any extra information is much appreciated. Thanks

 

[tiny-tim]

Welcome to PF!

3) The equation I am using is T= 2pi* sqrt ((4ML^3)/(Ebd^3)). Now this equation works out the time period of the vibrations, but if the time period is changing what does this equation work out?

Hi singh246! Welcome to PF!

Don't do it long enough for the time period to change!

4) I am planning to set up the experiment as shown in the link, but how would I set the cantilever into motion in order to make the formula work. Do I just let the mass at the end of the cantilever drop?

Just sellotape it on, and then, as the link says, "twang" it!.

(Twang it different amounts to get different amplitudes.)

It's not rocket science …

no special twanging training needed! ​

 

[Moetasim]

1) Yes, the amplitude of a cantilever can affect the time period of each oscillation in an experiment like the one described in the link.

2) The amplitude of a cantilever is the maximum displacement of the free end from its equilibrium position. When the amplitude is increased, the distance the cantilever travels during each oscillation also increases. This means that the time taken for one complete oscillation, or the time period, will also increase. This can be seen in the equation given, where the time period is directly proportional to the square root of the amplitude. Therefore, changing the amplitude will change the time period of each oscillation.

3) The equation you are using calculates the time period of the vibrations based on the mass, length, and elastic properties of the cantilever. It is a fundamental equation in mechanics and is used to determine the natural frequency of a system, which is the frequency at which the system will oscillate without any external forces. In this case, it is used to determine the time period of the cantilever's oscillations.

4) To set the cantilever into motion, you can use a variety of methods such as pulling the free end and releasing it, or attaching a motor to the free end to provide a continuous motion. In the experiment described in the link, the cantilever is set into motion by pulling the free end and releasing it, allowing it to oscillate freely. The formula will then work to calculate the time period of each oscillation. It is important to make sure the cantilever is not disturbed and allowed to oscillate freely in order to obtain accurate results.