A point performs simple harmonic oscillation of period $\mathrm{T}$ and the equation of motion is given by $x=a \sin (w t+\pi / 6)$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

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Aicharya · Accepted Answer

$\begin{aligned} & v=\omega \cos \left(\omega t+\frac{\pi}{6}ight) \ & \Rightarrow \quad \frac{\omega a}{2}=\omega \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{6}ight) \ & \Rightarrow \quad \frac{\pi}{3}=\frac{2 \pi}{T} t+\frac{\pi}{6} \ & \Rightarrow t=\frac{T}{12} \end{aligned}$ *

A point performs simple harmonic oscillation of period $\mathrm{T}$ and the equation of motion is given by…

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