An automobile's suspension system determines the vehicle's response to inputs from uneven road surfaces. Figure 3.56 shows a drawing of a suspension system that includes a coil spring, a shock absorber, and connecting links to the car frame and the wheel. Next to this artist's rendering is a simple model that can be used to estimate the vertical oscillations of the system. From a static state, the system is given an initial velocity of \(\dot{x}(0)=15 \mathrm{~m} / \mathrm{s}\). Calculate the response \(x(t)\) of the simplified system for the following parameter values: \(m=40 \mathrm{~kg}, k=25 \mathrm{kN} / \mathrm{m}\), and \(c=2.4 \mathrm{kN}-\mathrm{s} / \mathrm{m}\). There are no external forces acting on the wheel.

Transcribed Image Text:

A m k Figure 3.56: A cross section of an automotive suspension system consisting of a coil spring, a shock absorber, and connecting links to the car frame and the wheel. Next to this sketch is a single degree-of-freedom simplified model.