A one-degree-of-freedom model of a suspension system is shown in Figure P3.61(a). Consider a model in which the tire is modeled by a viscous damper of damping coefficient \(c_{t}\) and is placed in series with the spring and viscous damper modeling the suspension system, as illustrated in Figure P3.61(a).

(a) Derive a third-order differential equation governing the displacement of the vehicle from the system's equilibrium position.

(b) A plot of the suspension system when the wheel encounters a pothole is given in Figure P3.61(b). The plot is made for a suspension system that is designed to have a damping ratio of 0.1 . Use this information to find \(c_{t}\).

Transcribed Image Text:

m J 1.5 1.4 =0.1 1.3 2mk, 1.2 4/(1) 1.1 1 Cs 0.9 0.8 (a) FIGURE P3.61 0.7 0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 t(s) (b)