A quarter-car representation of a certain car has a stiffness k = 2000 lb/ft, which is the series combination of the tire stiffness and suspension stiffness, and a damping constant of c = 360 lb-sec/ft. The car weighs 2000 lb. Suppose the road profile is given (in feet) by y(t) = 0.03 sin (t, where the amplitude of variation of the road surface is 0.03 ft. and the frequency ( depends on the vehicle's speed and the road profile's period. Suppose the period of the road surface is 20 ft. Compute the steady-state motion amplitude and the force transmitted to the chassis, if the car is traveling at speeds of 20 and 50 mi/hr.