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in Physics by (34.9k points)
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Velocity and displacement of a body executing S.H.M. are out of phase by π/2. Why?

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Let displacement on y-axis is given by

y = asin ωt

Where a is the amplitude, ω is the angular velocity and  t is the instantaneous time.

Then velocity is given by

v = \(\frac{dy}{dt}\) = aω cos aω = aω sin ( \(\frac{\pi}{2}\) + aω)

The above equation clearly show that displacement and velocity of a body executing S.H.M. are out of phase by \(\frac{\pi}{2}\).

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