Consider the solenoid system of Problem 3.30. Assume the following parameter values: L0 = 4.0mH a = 2.2cm R = 1.5Ω K0 = 3.5N/cm. The plunger has mass M = 0.2 kg. Assume the coil to be connected to a dc source of magnitude 4 A. Neglect any effects of gravity.

a. Find the equilibrium displacement X0.

b. Write the dynamic equations of motion for the system.

c. Linearize these dynamic equations for incremental motion of the system around its equilibrium position.

d. If the plunger is displaced by an incremental distance E from its equilibrium position X0 and released with zero velocity at time t = 0, find (i) The resultant motion of the plunger as a function of time, and (ii) The corresponding time-varying component of current induced across the coil terminals.