For the system shown in Fig. 5.6, \(m_{1}=1 \mathrm{~kg}, m_{2}=2 \mathrm{~kg}, k_{1}=2000 \mathrm{~N} / \mathrm{m}, k_{2}=1000 \mathrm{~N} / \mathrm{m}\), \(k_{3}=3000 \mathrm{~N} / \mathrm{m}\), and an initial velocity of \(20 \mathrm{~m} / \mathrm{s}\) is imparted to mass \(m_{1}\). Find the resulting motion of the two masses.

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00000 k = k x(t) m 00000 = m k = nk X(1) m2 00000 m k3 = k FIGURE 5.6 Two-degree- of-freedom system.