A car is modeled with a capability of pitch and bounce motions, as shown in Fig. 5.45. It travels on a rough road whose surface varies sinusoidally with an amplitude of \(0.05 \mathrm{~m}\) and a wavelength of \(10 \mathrm{~m}\). Derive the equations of motion of the car for the following data: mass \(=1000 \mathrm{~kg}\), radius of gyration \(=0.9 \mathrm{~m}, \quad l_{1}=1.0 \mathrm{~m}, \quad l_{2}=1.5 \mathrm{~m}, \quad k_{f}=18 \mathrm{kN} / \mathrm{m}, \quad k_{r}=22 \mathrm{kN} / \mathrm{m}\), velocity \(=50 \mathrm{~km} / \mathrm{h}\).

Transcribed Image Text:

Bounce C.G. Pitch +0000, (a) -Reference x C.G. kr (b) FIGURE 5.45 Car with pitch and bounce motions.