Find the angular displacements \(\theta_{1}(t)\) and \(\theta_{2}(t)\) of the system shown in Fig. 5.58 for the initial conditions \(\theta_{1}(t=0)=\theta_{1}(0), \theta_{2}(t=0)=\theta_{2}(0)\), and \(\dot{\theta}_{1}(t=0)=\dot{\theta}_{2}(t=0)=0\).

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k 02 FIGURE 5.58 Two rotors connected by a shaft.