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A particle executing S.H.M. of amplitude $4 \mathrm{~cm}$ and $T=4 \mathrm{sec}$. The time taken by it to move from positive extreme position to half the amplitude is
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$2 / 3 \mathrm{sec}$
Equation of motion $y=a \cos \omega t$
$\begin{aligned} & \Rightarrow \frac{a}{2}=a \cos \omega t \Rightarrow \cos \omega t=\frac{1}{2} \Rightarrow \omega t=\frac{\pi}{3} \\ & \Rightarrow \frac{2 \pi t}{T}=\frac{\pi}{3} \Rightarrow t=\frac{\frac{\pi}{3} \times T}{2 \pi}=\frac{4}{3 \times 2}=\frac{2}{3} \mathrm{sec}\end{aligned}$
$\begin{aligned} & \Rightarrow \frac{a}{2}=a \cos \omega t \Rightarrow \cos \omega t=\frac{1}{2} \Rightarrow \omega t=\frac{\pi}{3} \\ & \Rightarrow \frac{2 \pi t}{T}=\frac{\pi}{3} \Rightarrow t=\frac{\frac{\pi}{3} \times T}{2 \pi}=\frac{4}{3 \times 2}=\frac{2}{3} \mathrm{sec}\end{aligned}$
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