Area, \(A=3 \times 10^{-4} m ^{2}\)

Angular speed, \(\omega=31.4 rad / s\)

\(T=\frac{2 \pi}{\omega}\)

\(I = I _{0} \cos ^{2} \omega t\)

\(\because \cos ^{2} \theta =\frac{1}{2},\) in one time period

\(I=\frac{E}{A\cdot t}\)

\(\therefore\) Average energy \(=\frac{I_{0}}{2} \cdot \frac{2 \pi}{\omega} A=\frac{3.3 \times 3.14 \times 3 \times 10^{-4}}{31.4}=9.9 \times 10^{-5} \)

\(\approx 10 \times 10^{-5} \approx 1 \times 10^{-4} J\)