Using the matrix iteration method, find the natural frequencies and mode shapes of the system shown in Fig. 6.6 with \(k_{1}=k, k_{2}=2 k, k_{3}=3 k\), and \(m_{1}=m_{2}=m_{3}=m\).

Figure 6.6:-

k k3 m3 (a) k x = 1 -x2=0 X3 = 0 k3 000 m m2 000 m3 k11 K21 K31 (b) k |2(x-x1)| 1k3(x3x2) m3 m m2 =k = -k = 0 k11 k21 K31 (c) -x = 0 x2 = 1 x3 = 0 k k2 kz 000 m 00000 m2 m3 K12 K22 K32 (d)