The dynamic system shown in Fig. 2 starts motion from the equilibrium position that corresponds to x = 0 and y=0. The mass moment of inertia of the rotating pulley about the stationary pivot is I and its radius is r; pulley in planar motion is considered massless. The solid homogenous disk of mass m and radius R rolls without slipping. Its mass moment of inertia about its center of mass (geometric center of the disk) is I = mR. The coefficient of friction is not known. The angle o of the incline is also not known. Motion of the disk is constrained by a spring with the stiffness coefficient k, and a damper with the damping coefficient d. While moving, block m slides along the vertical surface, experiencing viscous friction force proportional to block velocity. Viscous friction coefficient is c. wwww d D R m R I=0, Io cm1 'X Derive the governing equation(s) in terms of the displacement of the block x.