AP Physics Free Response Question

Question

A simple pendulum consists of mass m attached to a massless string. When the mass is displaced slightly from equilibrium position and released, the period swings back and forth with a frequency f. What is the frequency if mass 2m is attached to the string instead?

Answer 1

The period of a simple pendulum is given by:

for small angles only

T=2π (L/g)^1/2

Which depends on the Length of the pendulum L and the acceleration due to gravity, mass has nothing to do here.

Answer 2

The angular frequency of a pendulum relies primarily on two things - the length of the pendulum to the center of mass, and the gravitational acceleration, which provides the restoring force. To some small extent, angle also matters, but the small angle approximation cancels out that effect in basic Physics. Therefore, if you're only doubling the mass and not the location of the mass, then the change has no effect on the frequency.