Two cantilever beams of same material & cross-section have lengths $l$ and $2l$. Find the ratio of their first natural frequencies (round off to nearest integer).
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Correct Answer: 4
Solution and Explanation
\[ \frac{f_1(\text{Beam 1})}{f_1(\text{Beam 2})} = \frac{1/l^2}{1/(2l)^2} = \frac{1/l^2}{1/4l^2} = 4. \] Hence, the ratio is \(4\).
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Courage : Bravery :: Yearning :
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