Consider the two-degree-of-freedom quarter-car model shown in Figure 5.34, in which the force \(f\), applied between the car body and the wheel-tire-axle assembly, is controlled by feedback and represents the active components of the suspension system. Assume that \(f=20568 x_{1}-30493 x_{2}-1278 \dot{x}_{1}+3189 \dot{x}_{2}\). Build a block diagram of the feedback control system, where the quarter-car model is constructed using Simscape blocks and the controller is constructed using Simulink blocks. Find the displacement responses \(x_{1}(t)\) and \(x_{2}(t)\) if initially \(x_{1}=-0.05 \mathrm{~m}\) and \(x_{2}=-0.05 \mathrm{~m}\). Ignore the displacement input \(z(t)\). What are the system responses \(x_{1}(t)\) and \(x_{2}(t)\) without control?

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elle m2 x1 (a) FIGURE 5.34 A quarter-car model: (a) physical system and (b) free-body diagram. m x1 k (xx) f(x) (b) x2 m2 k2(x-2)