# Simple pendulum period depends on length, amplitude, gravity

Consider an ideal pendulum consisting of a "bob" of mass m hanging from a light (massless) string of length L. The pendulum swings back and forth in simple harmonic motion (SHM). You may assume that the oscillations are small, so that the motion is "ideal" SHM. Which of the following statements are true?

1. If the string length is changed to 4L, the frequency will increase by a factor of 2.

2. If the initial amplitude doubles, the frequency will also double.

3. To deduce the value of g (accel. due to gravity), you would need to know the mass of the pendulum bob

4. If the mass of the pendulum bob is changed to 4m, the frequency will decrease by a factor of 2

5. If the pendulum is moved to Jupiter, the frequency will increase.

* Please Provide a detailed explanation of why it is True/False

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#### Solution Preview

The period T, of an ideal simple pendulum of length L, in gravity field g, is expressed by: (1) T = 2 pi x Sqrt(L/g)

The frequency f, being the reciprocal of the period is: (2) f = 1/(2 pi) x Sqrt (g/L)

Question 1. False If the length is changed to 4L, the new frequency f' is ...

#### Solution Summary

The expert determines how a simple pendulum (small mass suspended by a cord) has a frequency which is depends on its length, amplitude and the surrounding gravity field.