One of the wheels and leaf springs of a car, traveling over a rough road, is shown in Fig. 5.30. For simplicity, all the wheels can be assumed to be identical and the system can be idealized as shown in Fig. 5.31. The car has a mass of \(m_{1}=1000 \mathrm{~kg}\) and the leaf springs have a total stiffness of \(k_{1}=400 \mathrm{kN} / \mathrm{m}\). The wheels and axles have a mass of \(m_{2}=300 \mathrm{~kg}\) and the tires have a stiffness of \(k_{2}=500 \mathrm{kN} / \mathrm{m}\). If the road surface varies sinusoidally with an amplitude of \(Y=0.1 \mathrm{~m}\) and a period of \(l=6 \mathrm{~m}\), find the critical velocities of the car.

Transcribed Image Text:

FIGURE 5.30 Wheel and leaf spring arrangement.