It is desirable to control the angular velocity w(t) of a rotor turbine of moment of inertia J=60 kgm2. The rotational motion of the rotor is excited by a step input torque TEng 50 N-m, generated by an engine. It is assumed that the rotor experiences a linear damping torque proportional to the angular velocity of the rotor and the coefficient of proportionality is DL=10 N-m-s/rad. The rotor also experiences a nonlinear damping torque whose mathematical form is quadratic i.e the magnitude of the torsional damping torque is proportional to the square of the angular velocity of the rotor. The coefficient of proportionality for the nonlinear damping is DNL 20 Nm-s/rad. 2.1. 2.2. 2.3. 2.4. Providing the free body diagram of the rotor turbine, derive the differential equation of motion of the rotor turbine Derive the expression for the angular velocity w(t) of the rotor turbine. Construct a detailed block diagram to control the angular velocity w(t) of the rotor turbine. (9) Assuming the final value of the time response for the angular velocity of the system to be reached when the maximum value is attained, calculate the final angular velocity of the rotor turbine. (6) (3) (4)