Lets say I have a brass rod of length L, and then a brass ball attached by a string so that both objects are the same length, the brass rod and the ball on a string have the same length. Now i will pull them back to the same point an let them oscillate like a pendulum. Why do they have different periods? Their centers of masses are at different places, is this the reason why? Is gravity acting on their center of masses over different distances? And they are both allowed to rotate from the top of their frame.