Period Does Not Depend on Mass

In the last section, we discovered that the period of a pendulum of length $\ell$ is $$T = 2\pi \cdot \sqrt {\frac {\ell}{g}},$$ which does not depend on the mass, $m$, of the bob. This seems unbelievable but is true and quite important to note. In fact, this was the motive of the famous now-compared-with-Miley-Cyrus experiment done by Prof. Walter Lewin. You can read more about the Galileo version of the intuition for this here.

period doesn't depend on mass, it's true, but period does depend on center of mass. if you change the mass of a certain object without changing it's lenght, diameter and volume, letting it in its past shape, be sure that period won't change. but if you change the mass and its those things, the center of mass is going to change and thus the working length of the pendulum will change and the center of mass will also change as the square of the period of a simple harmonic pendulum is equilibrium to the working lenght of a pendulum.