Chapter 9, Problem 70E

The physical behavior of automotive suspension systems is similar to an RLC circuit. The differential equation is defined by

$m\frac{d^{2}p(t)}{d{t}^2}+\mu f\frac{dp(t)}{dt}+Kp(t)=0$

where p(t) is the position variable of a piston in the cylinder of a shock absorber, m is the mass of the wheel, μ_f is the coefficient of friction, and K is the spring constant. The equivalent circuit representation is shown in Fig. 9.64. Suppose that the suspension is in its initial position at t = 0 (p(0) = 0), but it experiences a bump such that dp/dt at t = 0 is $\frac{1}{15}$ m/s. Use the equivalent circuit analogy and either MATLAB or SPICE to plot p(t) for the cases where μ_f = 300, 750, and 1500 N·s/m. The system has a spring constant of K = 22 kN/m and wheel mass of m = 30 kg.

■ FIGURE 9.64