Which of the following is a necessary and suf | vedclass

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(D) The defining characteristic of $Simple \ Harmonic \ Motion$ $(S.H.M.)$ is that the restoring force $F$ acting on the particle is directly proporti

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Proportionality between restoring force and displacement from equilibrium position

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(D) The defining characteristic of $Simple \ Harmonic \ Motion$ $(S.H.M.)$ is that the restoring force $F$ acting on the particle is directly proportional to its displacement $x$ from the equilibrium position and is directed towards the equilibrium position.Mathematically,this is expressed as $F = -kx$,where $k$ is the force constant.Since $F = ma$,this implies $a = -(k/m)x$,which means acceleration is also proportional to displacement.However,the fundamental physical condition that defines the motion is the linear restoring force,making option $(d)$ the necessary and sufficient condition.

Which of the following is a necessary and sufficient condition for $S.H.M.$?

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