Answer
$f$ = 50 Hz
Work Step by Step
Newton's law of motion state that
\begin{align*}
F = m a_{m}\\
k x_m = m (\omega^{2} x_{m} ) \\
k x_m = m \left( 2\pi f \right)^2 x_{m} \\
k =4 \pi^{2} m f^{2}
\end{align*}
The frequency will be solved by
\begin{gather*}
k=k_{r}+k_{l}\\
4 \pi^{2} m f^{2} = 4 \pi^{2} m f_r^{2} +4 \pi^{2} m f_l^{2}\\
f = \sqrt{f_r^2 + f_l^2 }
\end{gather*}
Substitute to get $f$
\begin{align*}
f &=\sqrt{f_{r}^{2}+f_{l}^{2}} =\sqrt{(30 \mathrm{~Hz})^{2}+(45 \mathrm{~Hz})^{2}} = \boxed{54 \mathrm{~Hz} }
\end{align*}
