Question

A simple pendulum consists of a mass M attached to a string oflength L andnegligible mass. For this system, when undergoing smalloscillations,a) the frequency is proportional to the amplitude.b) the period is proportional to the amplitude.c) the frequency is independent of the mass M.d) the frequency is independent of the length L

Answer 1

The frequency of the pendulum is independent of the mass on the end. (c)

This means that it doesn't matter if you hang a piece of spaghetti or a school bus from the bottom end.  If there is no air resistance, and no friction at the top end, and the string has no mass, then the time it takes the pendulum to swing from one side to the other only depends on the length of the string.