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The periodic time of a particle doing simple hormonic motion is $4 \mathrm{~s}$. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is
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Verified Answer
The correct answer is:
$\frac{1}{3} s$
$y=A \sin \left(\frac{2 \pi}{T}\right) t$
$$
\begin{array}{ll}
\Rightarrow & \frac{A}{2}=A \sin \left(\frac{2 \pi}{4}\right) t \\
\Rightarrow & \frac{\pi t}{2}=\frac{\pi}{6} \\
\Rightarrow & t=\frac{1}{3} \mathrm{~s}
\end{array}
$$
$$
\begin{array}{ll}
\Rightarrow & \frac{A}{2}=A \sin \left(\frac{2 \pi}{4}\right) t \\
\Rightarrow & \frac{\pi t}{2}=\frac{\pi}{6} \\
\Rightarrow & t=\frac{1}{3} \mathrm{~s}
\end{array}
$$
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