b
In \(SHM,\) velocities of a particle at distances \(x_{1}\) and \(x_{2}\) from mean position are given by

\({V_{1}^{2}=\omega^{2}\left(a^{2}-x_{1}^{2}\right)}...(i)\)

\({V_{2}^{2}=\omega^{2}\left(a^{2}-x_{2}^{2}\right)}...(ii)\)

From equations \((i)\) and \((ii),\) we get

\(V_{1}^{2}-V_{2}^{2}=\omega^{2}\left(x_{2}^{2}-x_{1}^{2}\right)\)

\(\omega=\sqrt{\frac{V_{1}^{2}-V_{2}^{2}}{x_{2}^{2}-x_{1}^{2}}} \)

\(T=2 \pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{V_{1}^{2}-V_{2}^{2}}}\)