(1 point) an 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. assume 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+π4) 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′′). 8y''+4y'+40y=4cos(2t+pi/4) the amplitude of the steady-state solution is sqrt(2)/4 m. the period of the steady-state solution is .33983 radians.