A bronze ball of mass \(m_{0}\) is dropped on the mass of a single-degree-of-freedom system from a height \(h\) as shown in Fig. 4.71. If the ball is caught after its first bounce, determine the resulting displacement response of the mass \(M\). Assume that the collision is perfectly elastic and the system is at rest initially. Data: \(M=2 \mathrm{~kg}, m_{0}=0.1 \mathrm{~kg}, k=100 \mathrm{~N} / \mathrm{m}, c=5 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), and \(h=2 \mathrm{~m}\).

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mo M 000000 x(t) FIGURE 4.71 Dropping of ball on damped system.