The general displacement of a simple harmonic oscillator is x= A sin ω t. Let T be its time period. The slope of its potential energy ( U ) - time (…

The general displacement of a simple harmonic oscillator is $\displaystyle x=\mathrm{A} \sin \omega \mathrm{t}$. Let T be its time period. The slope of its potential energy $\displaystyle (\mathrm{U})$ - time ( t ) curve will be maximum when $\displaystyle \mathrm{t}=\frac{\mathrm{T}}{\beta}$. The value of $\displaystyle \beta$ is $\displaystyle \_\_\_\_$.