Show all details. Use tables of Laplace transform and/or partial fraction expansion method to solve these problems. (Tables will take less time). Q1. Experiments were performed to understand motion of ship tied in a river. Apparatus consists of a long tank where flowing water and wave generator creates forces on the tied ship. The differential equation of motion of ship is given by: M d’x/d’t + C dx/dt + Kx = f + f2*exp(-2t) t> 0 (a) Find x(t) when M = 5.6, C = 4, K = 5, step function f = 4.6, f2 = 3, x(t=0)=1 and dx/dt (t=0)= 1 (b) Find the order of X(s) and the number of poles. Find all poles of X(s). Determine the stability of system. (c) Find damped and un-damped frequency of oscillation, steady state value of x(t) (which equals Xss) using final value theorem and form expression of x(t).