Question: A uniform beam, simply supported at both ends, is found to vibrate in its first mode with an amplitude of (10 mathrm{~mm}) at its center.

A uniform beam, simply supported at both ends, is found to vibrate in its first mode with an amplitude of $10 \mathrm{~mm}$ at its center. If $A=120 \mathrm{~mm}^{2}, I=1000 \mathrm{~mm}^{4}, E=20.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$, $ho=7.83 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, and $l=1 \mathrm{~m}$, determine the maximum bending moment in the beam.

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