A physical pendulum is constructed from a uniform thin rod of length L suspended from one end. The center of gravity for such a rod lies at the midpoint of its length.
1) Derive the equation of motion for this physical pendulum and, from that, determine its period and angular frequency, assuming only small angle oscillations.
2) What is the length of a simple pendulum that has this same period?
Hint: Gravity is the only force acting on the pendulum and, by definition, can be considered to be acting at its center of gravity.