Problem 4.55

A uniform cylindrical pulley of mass $M$ and radius $R$ can freely rotate about the horizontal axis $O$ (Fig. 4.17 ). The free end of a thread tightly wound on the pulley carries a deadweight $A$. At a certain angle $\alpha$ it counterbalances a point mass $m$ fixed at the rim of the pulley. Find the frequency of small oscillations of the arrangement.