A compressed air cylinder is connected to the spring-mass system shown in Fig. 4.45(a). Due to a small leak in the valve, the pressure on the piston, \(p(t)\), builds up as indicated in Fig. 4.45(b). Find the response of the piston for the following data: \(m=10 \mathrm{~kg}, k=1000 \mathrm{~N} / \mathrm{m}\), and \(d=0.1 \mathrm{~m}\).

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Valve Compressed air cylinder p(t), kPa Hose x(t) p(t) m p(t) = 50 (1-e) (b) FIGURE 4.45 Varying pressure acting on piston.