The small sphere of mass \(m\) is mounted on the light \(\operatorname{rod}\) pivoted at \(O\) and supported at end \(A\) by the vertical spring of stiffness \(k\). End \(A\) is displaced a small distance \(y_{0}\) below the horizontal equilibrium position and released. By the energy method, derive the differential equation of motion for small oscillations of the rod and determine the expression for its natural frequency \(\omega_{n}\) of vibration. Damping is negligible.

Transcribed Image Text:

b 1 m