Grandfather's (physical pendulum) Clock

A Grandfather clock's pendulum is constructed from a thin rod of negligible mass inserted into a uniform disk of mass $M = 1$ kg and radius $R = 5$ cm. The rod has a length $L$ from the pivot point to the center of the disk that can be adjusted from 0.20 m to 0.30 m in length so that the clock keeps the correct time.

a) Algebraically determine the (differential) equation of motion for the system, making the small angle approximation to put it in the form of a simple harmonic oscillator equation.

b) The clock keeps correct time when the period of its pendulum is $T = 1$ second. What should $L$ be (to 3 digits) so that this is true. (Use the algebraic form for $\omega^2$ from your answer to part a to solve for $L$.)