Answer to Question #122636 in Mechanics | Relativity for Bob Bell

Question

A simple pendulum is created using a object of mass 0.723 kg attached to a string of length 1.43 m and negligible mass. The object is pulled back 3.00 cm and released. The experiment is being done near the surface of the Earth.
What is the period of the pendulum?

What is the frequency of oscillation of the pendulum?

Answer 1

The period of a simple pendulum is

$$T=2\pi\sqrt\frac{l}{g}=2\pi\sqrt\frac{1.43}{9.8}=2.4\text{ s}.$$

The period does not depend on mass. For small initial displacements (3 cm is negligible compared to 1.43 m) the formula gives exact values.

The frequency is reciprocal to the period:

$$f=\frac{1}{T}=\frac{1}{2.4}=0.42\text{ Hz}.$$