The suspension system of a car traveling on a bumpy road has a stiffness of \(k=5 \times 10^{6} \mathrm{~N} / \mathrm{m}\) and the effective mass of the car on the suspension is \(m=750 \mathrm{~kg}\). The road bumps can be considered to be periodic half-sine waves as indicated in Fig. 4.42. Determine the displacement response of the car. Assume the damping of the system to be negligible.

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= y(t) + sin 2t - 2 2cos 4t 1(3) cos 8t 3(5) cos 12t 5(7)