An 8-kg mass is attached to a spring hanging from ceiling and allowed to come to rest. Suppose that the spring constant is 40 N/m and the damping constant is 4 N-sec/m. At time t=0, an external force of F(t)=4cos(2t+(pi)4) is applied to the system. Formulate the initial value problem describing the motion of the mass and determine the amplitude and period of the steady-state solution. Let y(t) to denote the displacement, in meters, of the mass from its equilibrium position. Set up a differential equation that describes this system. (give your answer in terms of y,y',y'').