$\begin{aligned} & \cos \theta_0=1-\frac{\theta_0^2}{2}=0.9 \\ & \frac{\theta_0^2}{2}=0.1 \Rightarrow \theta_0=10.2=\frac{1}{\sqrt{5}}\end{aligned}$

$$ \begin{aligned} & f_{\max }=\frac{v+v^{\prime}}{v-v^{\prime}} f \\ & f_{\min }=\frac{v-v^{\prime}}{v+v^{\prime}} f \\ & \Delta f_{\max }=f_{\max }-f_{\min }=\frac{v+v^{\prime}}{v-v^{\prime}} f-\frac{v-v^{\prime}}{v+v^{\prime}} f \\ & =\frac{\left(v+v^{\prime}\right)^2-\left(v-v^{\prime}\right)^2}{v^2-v^{\prime 2}} f \\ & \Delta f_{\max }=\frac{4 v v^{\prime}}{v^2-v^{\prime 2}} f ..........(i) \end{aligned} $$

Here, $\mathrm{v}^{\prime}=\ell \Omega_{\max }$

$$ \begin{aligned} & =\ell \cdot \theta_0 \cdot \omega \quad(\omega=\text { angular frequency }) \\ & =\ell \theta_0 \sqrt{\frac{\mathrm{~g}}{\ell}} \\ & \mathrm{v}^{\prime}=\theta_0 \sqrt{\mathrm{~g} \ell} \\ & \mathrm{v}^{\prime}=\frac{1}{\sqrt{5}} \sqrt{10 \times 8} \\ & \mathrm{v}^{\prime}=4 \end{aligned} $$

Put in equation (i)

$$ \begin{aligned} & \Delta f_{\max }=\frac{4 \times 330 \times 4 \times 660}{330^2-4^2} \\ & \approx \frac{16 \times 330 \times 660}{330} \approx 32 \end{aligned} $$