A car moving on a rough road, in the form of a sinusoidal surface, is modeled as a springmass system, as shown in Fig. 9.41. The sinusoidal surface has a wave length of \(5 \mathrm{~m}\) and an amplitude of \(Y=1 \mathrm{~mm}\). If the mass of the car, including the passengers, is \(1500 \mathrm{~kg}\) and the stiffness of the suspension system \((k)\) is \(400 \mathrm{kN} / \mathrm{m}\), determine the range of speed \((v)\) of the car in which the passengers perceive the vibration. Suggest possible methods of improving the design for a more comfortable ride of the passengers.

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x(1) 1 = m 1500 kg km/h 00000 k = 400 kN/m L=5m FIGURE 9.41 Car moving on sinusoidal road. Y = 1 mm