Suppose that a car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6250 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 25000 lbs/foot.

a. Assume no damping and determine the period of oscillation of the vertical motion of the car.
b. After 10 seconds the car body is 5 inches above its equilibrium position and at the high point in its cycle. What were the initial conditions?
c. Now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of -83.2 lb-sec/in times the vertical velocity of the car body. Find the displacement y(t) from equilibrium if y(o)=0 in and y(0)= -10 in/sec.