Using Holzer's method, find the natural frequencies and mode shapes of the system shown in Fig. 6.14, with \(m_{1}=100 \mathrm{~kg}, m_{2}=20 \mathrm{~kg}, m_{3}=200 \mathrm{~kg}, k_{1}=8000 \mathrm{~N} / \mathrm{m}\), and \(k_{2}=4000 \mathrm{~N} / \mathrm{m}\).

Figure 6.14:-

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k k m 000 m2 000 m3 FIGURE 6.14 Semidefinite system.