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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 π/2 radian, then the equation of S.H.M. will be:

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$y = 0.5 \sin 5 πt$

$y = 0.5 \sin 4 πt$

$y = 0.5 \cos 5 πt$

$y = 0.5 \sin 2.5 πt$

answer is D.

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Detailed Solution

$y = a \sin (ω t + ϕ) = a \sin (\frac{2 π}{T} t + ϕ) \Rightarrow y = 0.5 \sin (\frac{2 π}{0.4} t + \frac{π}{2}) \Rightarrow y = 0.5 \sin (5 πt + \frac{π}{2}) = 0.5 \cos (5 πt)$

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