Which of the following statements is correct | vedclass

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(A) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.Velocity is the derivative of displacement with respect to time: $v = \frac{dx}{dt

Vedclass · Accepted Answer

Velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.

Vedclass · Answer

(A) In $S.H.M.$,the displacement is given by $x = A \sin(\omega t)$.Velocity is the derivative of displacement with respect to time: $v = \frac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin(\omega t + \frac{\pi}{2})$.Comparing the phases,the velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.Acceleration is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = -A\omega^2 \sin(\omega t) = A\omega^2 \sin(\omega t + \pi)$.Comparing the phases,the acceleration leads the displacement by a phase of $\pi$ radians (or lags by $\pi$ radians).Therefore,the correct statement is that velocity leads the displacement by a phase of $\frac{\pi}{2}$ radians.

Column-$I$	Column-$II$
$(a)$ $t = \frac{T}{8}$	$(i)$ $\theta = \frac{5\pi}{4}$
$(b)$ $t = \frac{5T}{8}$	$(ii)$ $\theta = \frac{3\pi}{2}$
	$(iii)$ $\theta = \frac{\pi}{4}$

Which of the following statements is correct for $S.H.M.$?

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