Solve this using differiential equations! ( 16 pts ) A mass of 1 slug stretches a spring 2 ft and comes to rest at equilibrium. The system is attached to a dashpot that imparts a damping force equal to eight times the instantaneous velocity of the mass. Find the equation of motion if an external force equal to
f(t)=8sin(4t)
is applied to the system beginning at time
t=0
.