A 96 lb weight stretches a spring 3.2 ft in equilibrium. It is attached to a dashpot with damping constant c=18\displaystyle {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 (in feet) for t>0\displaystyle {t}>{0}.

y(t)=\displaystyle {y}{\left({t}\right)}=