> Q. A particle executing $SHM$. The phase difference between acceleration and displacement is – LIVE ANSWER TODAY

Q. A particle executing $SHM$. The phase difference between acceleration and displacement is

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A particle executing $SHM$. The phase difference between acceleration and displacement is

Solution:

Let the displacement of a particle executing simple harmonic motion at any instant $t$ is, $x = A cos omega t$

Velocity, $v=frac{dx}{dt} = frac{d}{dt}left(A cos omega tright) = -Aomega sin omega t$

Acceleration, $a = frac{dv}{dt} = -A omega^{2} cos omega t $

$= Aomega^{2} cos left(omega t +piright) $

Phase of displacement, $phi_{1} = omega t $

Phase of acceleration, $phi_{2} = omega t +pi $

$ therefore$ Phase difference $= phi_{2} -phi_{1} $

$= left(omega t + piright)-omega t = pi$

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