a)Determine the mass m and the spring constant k, and give the differential equation describing the harmonic motion of this system.

b)Solve the differential equation and find the displacement y.
c) Assume that in addition an external force of 6e^-4t lb is applied, find the displacement for this new system.

An object weighing 32 lb stretches a spring 2ft in equilibrium. There is also a damping force with c = 8. The spring is raised 2 ft and thrown upwards with a velocity of 4ft/sec.