Determine the natural frequencies and mode shapes for the system of Figure P7.17 if (k=10,000 mathrm{~N} /

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Determine the natural frequencies and mode shapes for the system of Figure P7.17 if \(k=10,000 \mathrm{~N} / \mathrm{m}, m=3 \mathrm{~kg}, I=0.6 \mathrm{~kg} \cdot \mathrm{m}^{2}\), and \(r=80 \mathrm{~cm}\).

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