The periodic time of a body executing simple harmonic motion is $3\, sec$. After how much interval from time $t = 0$, its displacement will be half of its amplitude ..... $\sec$
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(c) $y = a\sin \frac{{2\pi }}{T}t$
==> $\frac{a}{2} = a\sin \frac{{2\pi t}}{3}$
==> $\frac{1}{2} = \sin \frac{{2\pi t}}{3}$
==> sin$\frac{{2\pi t}}{3} = \sin \frac{\pi }{6}$
==> $\frac{{2\pi t}}{3} = \frac{\pi }{6}$
==> $t = \frac{1}{4}\sec $
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