A mass m is suspended from a spring of negligible mass and the...

Frequency of oscillation of a spring-block system is given by, $f = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$

Therefore, for both cases, we can write

${f}_{1} = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$ and 

${f}_{2} = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{9m}}$

Required ratio, $\dfrac{{f}_{1}}{{f}_{2}} = \sqrt{\dfrac{9}{1}} = \dfrac{3}{1}$