Answer
$$
f=1.28 \mathrm{~Hz}
$$
Work Step by Step
$$
\begin{aligned}
& \phi=\frac{1.5 \theta_{\max }}{0.75} \\
& \Delta=0.75(1-\cos \phi) \\
& \cong 0.75\left(1-1+\frac{\phi^2}{2}\right) \\
& =0.75\left(\frac{4 \theta_{\max }^2}{2}\right) \\
& \Delta G=\frac{1}{2} \Delta=0.75 \theta_{\max }^2 \\
& T_{\max }=\frac{1}{2} I_A \omega_{\max }^2 \\
& =\frac{1}{2}\left[\frac{1}{3}\left(\frac{4(1.5)}{32.2}\right)(1.5)^2\right] \omega_n^2 \theta_{\max }^2 \\
& =0.0699 \omega_n^2 \theta_{\max }^2 \\
& V_{\max }=W \Delta_G=4(1.5)\left(0.75 \theta_{\max }^2\right) \\
& T_{\max }=V_{\max } \\
& 0.0699 \omega_n^2 \theta_{\max }^2=4.5 \theta_{\text {max }}^2 \\
& \omega_n^2=64.40 \\
& \omega_n=8.025 \mathrm{rad} / \mathrm{s} \\
& f=\frac{\omega_n}{2 \pi}=\frac{8.025}{2 \pi}=1.28 \mathrm{~Hz} \\
&
\end{aligned}
$$
