Determine the natural frequencies of the system of Figure P 6.4 if (I_{1}=0.3 mathrm{~kg} cdot mathrm{m}^{2}), (I_{2}=0.4

Question:

Determine the natural frequencies of the system of Figure P 6.4 if $I_{1}=0.3 \mathrm{~kg} \cdot \mathrm{m}^{2}$, $I_{2}=0.4 \mathrm{~kg} \cdot \mathrm{m}^{2}, J_{1}=J_{2}=1.6 \times 10^{-8} \mathrm{~m}^{4}, G_{1}=G_{2}=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$, and $L=30 \mathrm{~cm}$. Determine the modal fractions for each mode. Identify any nodes.

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