Two pulleys are driven by a belt as shown in Fig. 5.62. If the pulleys have radii \(r_{1}\) and \(r_{2}\) and mass moments of inertia \(J_{1}\) and \(J_{2}\), respectively, determine the natural frequencies of the pulley drive system. Assume the stiffness of the belt on each side as \(k\) as indicated in Fig. 5.62.

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belt k 2 k FIGURE 5.62 Two pulleys connected by belt.