For the system given in the figure, u(t) voltage is applied to the solenoid which is modeled as a system consists of a resistive and an inductive element. Solenoid generates a force u(t) which is a function of current and given as F(t)=K i(t). The mechanical system attached to the massless link AB is moved vertically due to this applied force. R W A L Li of Jo L2 B K M C arran X(t) a. Draw the block diagram of the system. Write the transfer function giving the relation between input voltage U(s) and the vertical displacement XB(S) b. If a constant 5V input voltage is applied, find the time expression for the force FB(t) that is effected to point B and also find the steady state value of this force c. Suppose that a constant force of IN is generated at the solenoid. Find natural frequency and the damping ratio of the mechanical subsystem d. For the conditions given in part c, obtain the steady state value of vertical displacement XB and also the settling time of the mechanical subsystem e. Find the equation of the motion of the system that makes oscillations about point O. Take selenoid current as input of the system. (R-50, L-0.1H, K-10 N/A, L/L-5, M-0.5kg, K-8N/m, C-INs/m)