Using Holzer's method, find the natural frequencies and mode shapes of the system shown in Fig. 6.39. Assume that \(J_{1}=10 \mathrm{~kg}-\mathrm{m}^{2}, J_{2}=5 \mathrm{~kg}-\mathrm{m}^{2}, J_{3}=1 \mathrm{~kg}-\mathrm{m}^{2}\), and \(k_{t 1}=k_{t 2}=\) \(1 \times 10^{6} \mathrm{~N}-\mathrm{m} / \mathrm{rad}\).

Figure 6.39:-

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kn k12 J3,03 J1,01 J2.02 FIGURE 6.39 Semidefinte torsional system.