Design the suspension of an automobile such that the maximum vertical acceleration felt by the driver in less than 2 g at all speeds between 40 and 50 mph while traveling on a road whose surface varies sinusoidally as y(u) = 0.5 sin 2*u ft, where u is the horizontal distance in feet. The weight of the automobile, with the driver, is 1500 lb and the damping ratio of the suspension is to be 0.5. Use a single-degree-of-freedom model for the automobile.