Question $8$ In the system shown in the static equilibrium position, a spring with a spring coefficient k is attached to point B $,$ and a viscous damper with a damping coefficient c is attached to point A $.$ The cylinder is hinged to the ground from the center of the mass. An inextensible rope is wound around the cylinder of mass $m$ and radius $R,$ and a rigid body with a mass of M is attached to the end of the rope. The rigid body is also connected to the ground with a viscous damper with a damping coefficient c$.$ Obtain the equation of motion of the small amplitude vibrations of the system around the static equilibrium position by constructing the equivalent system.