A mass $\mathrm{m}$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9 \mathrm{~m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_{.2}}$ is_____________.
JEE MAIN 2024, Diffcult
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$\mathrm{f}_1=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$
$\mathrm{f}_2=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{9 \mathrm{~m}}}$
$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{9}{1}}=\frac{3}{1}$
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