The variation of the acceleration a of a part | vedclass

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(C) In Simple Harmonic Motion $(S.H.M.)$,the acceleration $a$ of a particle is directly proportional to the negative of its displacement $x$ from the

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(C) In Simple Harmonic Motion $(S.H.M.)$,the acceleration $a$ of a particle is directly proportional to the negative of its displacement $x$ from the mean position.This relationship is given by the equation: $a = -\omega^2 x$,where $\omega$ is the angular frequency.This equation is of the form $y = mx$,which represents a straight line passing through the origin.Since the slope $m = -\omega^2$ is negative,the graph must be a straight line passing through the origin with a negative slope.Therefore,the correct graph is the one shown in option $C$.

The variation of the acceleration $a$ of a particle executing $S.H.M.$ with displacement $x$ is as shown in the figure. Which of the following graphs correctly represents this relationship?

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