Using Rayleigh's method, determine the first natural frequency of vibration of the system shown in Fig. 7.2. Assume \(k_{1}=k, k_{2}=2 k, k_{3}=3 k\), and \(m_{1}=m, m_{2}=2 m, m_{3}=3 m\).

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0000 x(1) mi x2(1) m2 0000 m3 X3(1) k FIGURE 7.2 Three- degree-of-freedom spring-mass system.