1. Frequency of a mass-spring system

For a spring of force constant $k$ and attached mass $m$, the frequency of simple harmonic motion is

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

2. For mass $m$

Given frequency is $f_1$, so

$f_1=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

3. For mass $9m$

Given frequency is $f_2$, so

$f_2=\frac{1}{2\pi}\sqrt{\frac{k}{9m}}$

Simplify:

$f_2=\frac{1}{2\pi}\cdot \frac{1}{3}\sqrt{\frac{k}{m}}$

4. Find the ratio $\frac{f_1}{f_2}$

$\frac{f_1}{f_2}=\frac{\frac{1}{2\pi}\sqrt{\frac{k}{m}}}{\frac{1}{2\pi}\sqrt{\frac{k}{9m}}}$

$\frac{f_1}{f_2}=\sqrt{\frac{k/m}{k/(9m)}}=\sqrt{9}=3$

5. Final answer

$\frac{f_1}{f_2}=3$

This matches the stored correct answer.