A lumped model of a machine-tool drive system is shown in Fig. 3. The system parameters are: Jm=15 Nmshad, Bm-2 Nms/rad, m=4kg, k=2N/m, R=0.10m. The stiffness of the shaft is represented by a linear spring constant ks = 0.2 Nmhad. You can assume the friction force between the ground and the block to be equivalent to viscous damping with a coefficient c=1 Nshn. A) Draw the free-body diagram of the mechanical system shown in Fig. 3 B) Write the necessary equations of motion of the system. C) Write the state-space model of the system assuming the outputs, θ, and 12 (angle of the input wheel and rotational speed of the pinion). 02 Pinion e, ks No friction Rack Input T(r)