Question 8.P.5: The aluminum beam shown in Figure P8.5 carries a small hoist...
The aluminum beam shown in Figure P8.5 carries a small hoist weighing 450 N. Calculate the frequency of vibration when the hoist is at a distance of 1.2 \mathrm{~m}. from one support. What are the lowest and highest frequencies and the corresponding hoist locations? E=69,000 \mathrm{MPa} and \rho=2770 \mathrm{~kg} / \mathrm{m}^{3} for aluminum.

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With an assumed vibration shape \psi(x)=\sin \pi x / L; hoist at 1.2 \mathrm{~m}, \omega=77.62 \mathrm{rad} / \mathrm{s} ; maximum frequency when hoist at support \omega=149.3 \mathrm{rad} / \mathrm{s} ; minimum frequency when hoist at mid-span \omega=69.62 \mathrm{rad} / \mathrm{s}.
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