A simple harmonic wave having an amplitude a and time period $T$ is represented by the equation $y = 5\sin \pi (t + 4)m.$ Then the value of amplitude $(a)$ in $(m)$ and time period $(T) $ in second are
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(d) $y = 5\sin (\pi \,t + 4\pi )$, comparing it with standard equation
$y = a\sin (\omega \,t + \phi ) = a\sin \left( {\frac{{2\,\pi \,t}}{T} + \phi } \right)$
$a = 5\,m$ and $\frac{{2\,\pi \,t}}{T} = \pi \,t$
$y = a\sin (\omega \,t + \phi ) = a\sin \left( {\frac{{2\,\pi \,t}}{T} + \phi } \right)$
$a = 5\,m$ and $\frac{{2\,\pi \,t}}{T} = \pi \,t$
==> $T = 2\, sec.$
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