\(K E=\frac{5}{4} P E\)

\(\frac{1}{2} m \omega^2\left(A^2-x^2\right)=\frac{5}{4} \times \frac{1}{2} m \omega^2 x^2\) \({\left[ v =\omega \sqrt{ A ^2- x ^2}\right]}\)

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

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

\(x=\frac{2}{3} A\)

\(\therefore x=\frac{2}{3} \times 3\,cm\)

\(x=2\,cm\)