Find the free-vibration response of the triple pendulum shown in Fig. 6.10 for \(l_{i}=l(i=1,2,3)\) and \(m_{i}=m(i=1,2,3)\) for the initial conditions \(\theta_{1}(0)=\theta_{2}(0)=0\), \(\theta_{3}(0)=\theta_{30}, \dot{\theta}_{i}(0)=0(i=1,2,3)\).

Figure 6.10:-

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41 m 2 y Y2 -x3- y m2 03 13 m3 FIGURE 6.10 Triple pendulum. x+