A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is (2 A)/3.…

A particle performs simple harmonic motion with amplitude $\displaystyle A$. Its speed is increased to three times at an instant when its displacement is $\displaystyle \frac{2 A}{3}$. The new amplitude of motion is $\displaystyle \frac{n A}{3}$. The value of $\displaystyle n$ is $\displaystyle \_\_\_\_$.