A cushion suspension, such as the driver's seat or a child seat in an automobile can be modeled as shown in Fig. 3.61. By assuming the support or base motion, \(y(t)\), as the input, derive the equations of motion for determining the responses \(x(t)\) and \(z(t)\). Combine the two equations of motion to derive a single differential equation in terms of only \(x(t)\).

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m x(t) z(t) K y(t), Input FIGURE 3.61 Driver's seat subjected to base motion.