Shown in Figure 2 is a thin disk of mass m, radius r, and rotary inertia I rolling without slipping on a rough surface with friction coefficient .

Shown in Figure 2 is a thin disk of mass m, radius r, and rotary inertia I rolling without slipping on a rough surface with friction coefficient μ. The disk is connected to the fixed surface through a spring with stiffness k and a damper with damping constant c. 

(i) Draw the free body diagram of the disk

(ii) Derive the equation of motion using Newton's 2nd law