Which one of the following equations of motio | vedclass

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(C) The defining condition for Simple Harmonic Motion $(S.H.M.)$ is that the acceleration $(a)$ is directly proportional to the negative of the displa

Vedclass · Accepted Answer

$Acceleration = -k(x+a)$

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(C) The defining condition for Simple Harmonic Motion $(S.H.M.)$ is that the acceleration $(a)$ is directly proportional to the negative of the displacement $(x)$ from the mean position.Mathematically,this is expressed as $a = -\omega^2 x$,where $\omega$ is the angular frequency.In option $(C)$,the equation is $a = -k(x+a)$. If we define a new coordinate $x' = x+a$,then the equation becomes $a = -k x'$.This represents an $S.H.M.$ about the equilibrium position $x = -a$.Since the acceleration is proportional to the displacement from the mean position and directed towards it,option $(C)$ correctly represents $S.H.M.$

Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

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