initial velocity

\(v^{2}=\omega^{2}\left(A^{2}-\left(\frac{2 A}{3}\right)^{2}\right)\)                \(...(1)\)

Where \(A\) is initial amplitude \(\&\, \omega\) is angular frequency.

Final velocity

\((3 v)^{2}=\omega^{2}\left(A^{\prime 2}-\left(\frac{2 A}{3}\right)^{2}\right)\)                \(...(2)\)

From equation \(\&\) equation \(( 2)\)

\(\frac{1}{9}=\frac{A^{2}-\frac{4 A^{2}}{9}}{A^{2}-\frac{4 A^{2}}{9}}\)

\(A^{\prime}=\frac{7 A}{3}\)