A mass weighing 16 pounds is attached to a 5-foot long spring. At equilibrium, the spring measures 8.2 feet (In Hooke's law Fs=kx, we need to replace it with 8.2-5=3.2 ft. If the mass is is initially released from rest at a point 2 feet above the equilibrium position, [x(0) = -2, x'(0)=0].

a)Find the displacement (Equation of the motion) if it is further known that the surrounding medium offers a resistance numerically equal to the instantaneous velocity (Fd=x'(t)

b) Is the motion, under-damped, over-damped, or critically damped? (Assume that the positive direction is downward)

c) Graph x(t) on [-1,5]