The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x(t)=A sin ω t, where A is the amplitude. The…

The displacement of a particle, executing simple harmonic motion with time period $\displaystyle T$, is expressed as $\displaystyle x(t)=A \sin \omega t$, where $\displaystyle A$ is the amplitude. The maximum value of potential energy of this oscillator is found at $\displaystyle t=T / 2 \beta$. The value of $\displaystyle \beta$ is $\displaystyle \_\_\_\_$.