Problem 4.46

An arrangement illustrated in Fig. 4.14 consists of a horizontal uniform disc $D$ of mass $m$ and radius $R$ and a thin rod $A O$ whose torsional coefficient is equal to $k .$ Find the amplitude and the energy of small torsional oscillations if at the initial moment the disc was deviated through an angle $\varphi_{0}$ from the equilibrium position and then imparted an angular velocity $\varphi_{0}$ .

\varphi_{m}=\varphi_{0} \sqrt{1+m R^{2} \dot{\varphi}_{0}^{2} / 2 k \varphi_{0}^{2}}, E=1 / 2 k \varphi_{m}^{2}

Mechanical Oscillations