The amplitude and the time period in a $S.H.M.$ is $0.5 \,cm$ and $0.4 \,sec$ respectively. If the initial phase is $\pi /2$ radian, then the equation of $S.H.M.$ will be
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(d) $y = a\sin (\omega \,t + \phi )$
$ = a\sin \left( {\frac{{2\pi }}{T}t + \phi } \right)$
$ = a\sin \left( {\frac{{2\pi }}{T}t + \phi } \right)$
$y = 0.5\sin \,\left( {\frac{{2\pi }}{{0.4}}t + \frac{\pi }{2}} \right)$
$y = 0.5\sin \,\left( {5\pi \,t + \frac{\pi }{2}} \right) = 0.5\cos 5\pi t$
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