A 96 lb weight stretches a spring 3.2 feet in equilibrium. It is attached to a dashpot with damping constant c = 18 lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement for t> 0 if the forcing function is F(t) = e-³t sin t.

A 96 lb weight stretches a spring 3.2 feet in equilibrium. It is attached to a dashpot with damping constant c = 18 lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement for t> 0 if the forcing function is F(t) = e-³t sin t.