Show that the governing equation of motion is as follows (M + m) + ml cos 06-ml0 sin 0 where ml cos b + ml6 mgl sin 0 = 0 b) (20 pts) Linearize the equations, find the transfer functions and state-space equations c) (10 pts) Consider unit parameter values and f-0. Construct the Simulink (or equivalent) block diagram for the system and draw the responses to nonzero initial states for the nonlinear system d) (10 pts) Consider unit parameter values and f-0. Construct the Simulink (or equivalent) block diagram for the system and draw the responses to nonzero initial states for the linearized system e) (20 pts) Consider the linearized model and that the rotary joint is attached to armature controlled DC motor having the following transfer functions G(s) = Ra () (s) U(s) - = 20 k, s(JRs + k,k + fR) k S(TS + 1) k, = 1 N-m/A k, = 3 V-s/rad y f Y2 W 0 m Z2