Let mass is displaced towards left by $x$ then force on mass
$=-k x-2 k x=-3 k x$
[negative sign is taken because force is opposite to the direction of motion]
$\Rightarrow F=-3 k x=-m \omega^{2} x$
$ \Rightarrow \omega=\sqrt{\frac{3 k}{m}}$
$f=\frac{\omega}{2 \pi}=\frac{1}{2 \pi} \sqrt{\frac{3 k}{m}}$
Thus it is proportional to $\sqrt{\frac{3 k}{m}}$
