Problem 4.54

Find the frequency of small oscillations of the arrangement illustrated in Fig. \(4.16 .\) The radius of the pulley is \(R,\) its moment of inertia relative to the rotation axis is \(I,\) the mass of the body is \(m\) and the spring stiffness is \(x .\) The mass of the thread and the spring is negligible, the thread does not slide over the pulley, there is no friction in the axis of the pulley.