Write a computer program for finding the eigenvectors using the known eigenvalues in \(\mathrm{Eq}\). (6.61). Find the mode shapes of Problem 6.57 using this program.

Data From Problem 6.57:-

Find the natural frequencies and mode shapes of the system shown in Fig. 6.29 for \(k_{1}=k_{2}=k_{3}=k_{4}=k, m_{1}=2 m, m_{2}=3 m\), and \(m_{3}=2 m\).

k k k3 KA 000 m 000 mmy 000 FIGURE 6.29 Spring-mass system.