A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x.
The aim is to derive a formula for the period T of small-amplitude oscillation versus the distance x.

Question

A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x.
The aim is to derive a formula for the period T of small-amplitude oscillation versus the distance x.

anonymous · Answer

There is a standard formula for the period of oscillation of a simple pendulum.
If you know how to find the centre of mass of your more complicated pendulum, you can treat it as a simple pendulum of mass 2M with a length determined by the position of its centre of mass, then you can use the standard formula to find the period.