The figure shown below depicts a vibratory system consists of a disc of mass mrolling on a smooth surface without slip. An additional block of mass 2m isconnected to a pulley so that the displacement of the centre of the disc fromequilibrium is x. If the pulley rotates with an angle , determine Keq and meq of thesystem.

A thin disc of mass m and radius r has a spring stiffness k and a viscous dampingcoefficient c attached to the discs centre, as shown in the figure. The mass momentof inertia of the disc is = .Derive the differential equation governing the displacement of the mass centre.