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.