The velocity of a particle in simple harmonic motion is given as

\(v=\omega \sqrt{A^{2}-x^{2}}\)

and magnitude of its acceleration is

\(a=\omega^{2} x\)

Given \(|v|=|a|\)

\(\therefore \omega \sqrt{A^{2}-x^{2}}-\omega^{2} x\)

\({\omega x=\sqrt{A^{2}-x^{2}} \text { or } \omega^{2} x^{2}=A^{2}-x^{2}}\)

\({\omega^{2}=\frac{A^{2}-x^{2}}{x^{2}}=\frac{9-4}{4}=\frac{5}{4}}\)

\({\omega=\frac{\sqrt{5}}{2}}\)

Time period, \(T=\frac{2 \pi}{\omega}=2 \pi \cdot \frac{2}{\sqrt{5}}=\frac{4 \pi}{\sqrt{5}} \mathrm{s}\)