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Design the suspension of an automobile such that the maximum vertical acceleration felt by the driver is less than 2g at all speeds between 40 and 80 mph while traveling on a road whose surface varies sinusoidally as 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 0.05. Use a single-degree-of-freedom model for the automobile.

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