Question

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).

Hint:

Natural frequency of a cantilever varies inversely with the square of its length.

Answer 1

Correct Answer: 4

For a cantilever beam: \[ f_1 \propto \frac{1}{L^2}. \] Thus:
\[ \frac{f_1(\text{Beam 1})}{f_1(\text{Beam 2})} = \frac{1/l^2}{1/(2l)^2} = \frac{1/l^2}{1/4l^2} = 4. \] Hence, the ratio is \(4\).