*PLEASE SHOW ALL WORK*
Consider a damped, forced mass/spring system. Let t denote time(in seconds) and let x(t) denote the position (in meters) of themass at time t, with x = 0 corresponding to the equilibriumposition. Suppose the mass m = 1 kg, the damping constant c = 3N·s/m, the spring constant k = 2 N/m, the external force is F (t) =20 cos(2t), the initial position
x(0) = 1 m, and the initial velocity x?(0) = 2 m/s. a. Find theposition function x(t).
b. What part of the solution is the transient part and what partis the steady-state part?
