Suppose that a car weighing 4000 pounds is supported by four shock absorbers each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. 1. assume no damping and determine the period of oscillation of the vertical motion of the car. hint: g=32 ft/sec2. t= 0.436 seconds. 2. after 10 seconds the car body is 1/3 foot above its equilibrium position and at the high point in its cycle. what were the initial conditions ? y(0) = 2.85 x ft. and y'(o) = ft/sec. 3. now assume that oil is added to each the four shock absorbers so that, together, they produce an effective damping force of - 6.93 lb-sec/ft times the vertical velocity of the car body. find the displacement y(t) from equilibrium if y(0)=0 ft and y'(o)=-10 ft/sec. xx) = 4.41e-0.027tsin (3.8t+r) *