\((I)=m\left(\frac{d}{2}\right)^{2} \times 2=\frac{m d^{2}}{2}\)

Now by \(\tau=1 \alpha\)

\((q E)(d \sin \theta)=\frac{m d^{2}}{2} \cdot \alpha\)

\(\alpha=\left(\frac{2 \mathrm{qE}}{\mathrm{md}}\right) \sin \theta\) for small \(\theta\)

\({\Rightarrow \alpha=\left(\frac{2 \mathrm{qE}}{\mathrm{md}}\right) \theta}\)

\(\Rightarrow \) Angular frequency \(\omega  = \sqrt {\frac{{2qE}}{{md}}} \)