A mass mathrm{m} is suspended from a spring of negligible mass and system oscillates with a frequenc

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13.Oscillations

hard

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_____________.

A

$3$

B

$4$

C

$5$

D

$6$

(JEE MAIN-2024)

Solution

$\mathrm{f}_1=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

$\mathrm{f}_2=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{9 \mathrm{~m}}}$

$\frac{\mathrm{f}_1}{\mathrm{f}_2}=\sqrt{\frac{9}{1}}=\frac{3}{1}$

Standard 11

Physics

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