Use a two element, finite element model to approximate the two lowest torsional natural frequencies for the system of Figure P11 14 begin aligned J 3 2 times 10 5 mathrm m 4 G 80 times 10 9 mathrm N mathrm m 2 ho 7000 mathrm kg mathrm m 3 L 4 2 mathrm m I 1 5 mathrm kg cdot mathrm m 2 end aligned FIGURE P11 14 FIGURE P11 14 L I

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Question: Use a two-element, finite-element model to approximate the two lowest torsional natural frequencies for the system of Figure P11.14. [ begin{aligned} & J=3.2 times 10^{-5}

Use a two-element, finite-element model to approximate the two lowest torsional natural frequencies for the system of Figure P11.14.

FIGURE P11.14 L I

\[ \begin{aligned} & J=3.2 \times 10^{-5} \mathrm{~m}^{4} \\ & G=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2} \\ & ho=7000 \mathrm{~kg} / \mathrm{m}^{3} \\ & L=4.2 \mathrm{~m} \\ & I=1.5 \mathrm{~kg} \cdot \mathrm{m}^{2} \end{aligned} \]

FIGURE P11.14

FIGURE P11.14 L I

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