# Physical Pendulum: Derive the equation for the period, the angular frequency and the length of a simple pendulum

A physical pendulum is constructed from a uniform thin rod of length L suspended from one end. The center of gravity lies at the midpoint of it's length.

1) Derive the equation for the period of this physical pendulum, assuming only small angle oscilllations.

2) Derive the equation for the angular frequency of this physical pendulum, again assuming small angle oscillations.

3) What would be the length of a simple pendulum that has this same period?

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#### Solution Preview

A physical pendulum is constructed from a uniform thin rod of length L suspended from one end. The center of gravity lies at the midpoint of it's length.

1) Derive the equation for the period of this physical pendulum, assuming only small angle oscillations.

2) Derive the equation for the angular frequency of this physical pendulum, again assuming small angle oscillations.

3) What would be the length of a ...

#### Solution Summary

This solution provides an explanation and a graph, with formulas and calculations to solve the problems in an attached Word document.