Problem 1. (20 pts) The suspension system of a car traveling on a bumpy road has...

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Problem 1. (20 pts) The suspension system of a car traveling on a bumpy road has a stiffness of k = 5 106 N/m and the effective mass of the car on the suspension is m = 750 kg. The road bumps can be considered to 1 1 be periodic half-sine, y(t) = - + sin 2t 2 (cos 4t - + 2 1(3) COS 8t 3(5) + COS 12t 5(7) + ...}. Determine the displacement response of the car. Assume the damping of the system to be negligible. y(t) m 12 y(t) 00000 k x(t) 0.5T T 1.5T 2T 2.5T 3T t (time) Problem 1. (20 pts) The suspension system of a car traveling on a bumpy road has a stiffness of k = 5 106 N/m and the effective mass of the car on the suspension is m = 750 kg. The road bumps can be considered to 1 1 be periodic half-sine, y(t) = - + sin 2t 2 (cos 4t - + 2 1(3) COS 8t 3(5) + COS 12t 5(7) + ...}. Determine the displacement response of the car. Assume the damping of the system to be negligible. y(t) m 12 y(t) 00000 k x(t) 0.5T T 1.5T 2T 2.5T 3T t (time)