Set up the eigenvalue problem of Example 6.11 in terms of the coordinates \(q_{1}=x_{1}, q_{2}=\) \(x_{2}-x_{1}\), and \(q_{3}=x_{3}-x_{2}\), and solve the resulting problem. Compare the results obtained with those of Example 6.11 and draw conclusions.

Data From Example 6.11:-

Figure 6.12:-

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Find the natural frequencies and mode shapes of the system shown in Fig. 6.12 for k = k = k3 = k and m = m2 m3 = m.