An integral pulley shown in the below figure is restrained in its movement about its own axis by a torsional spring of stiffness K and a linear spring of stiffness k. A load of mass m is hung from the smaller pulley by means of an inextensible string. Using D Alembert’s principle derive the equation of motion for small oscillations and determine the natural frequency. Take J as mass moment of inertia of the pulley about its axis.
