In a linear simple harmonic motion (SHM):(A) | vedclass

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(A) In a linear simple harmonic motion $(SHM)$:$(A)$ The restoring force is given by $F = -kx$,which means the force is directly proportional to the d

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$(A), (B)$ and $(C)$ only

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(A) In a linear simple harmonic motion $(SHM)$:$(A)$ The restoring force is given by $F = -kx$,which means the force is directly proportional to the displacement $x$ and acts in the opposite direction. Thus,statement $(A)$ is true.$(B)$ The acceleration $a$ is given by $a = -\omega^2 x$. Since the acceleration is proportional to the negative of the displacement,they are always opposite in direction. Thus,statement $(B)$ is true.$(C)$ The velocity $v$ in $SHM$ is given by $v = \omega \sqrt{A^2 - x^2}$. At the mean position $(x = 0)$,the velocity is $v = \omega A$,which is the maximum value. Thus,statement $(C)$ is true.$(D)$ The magnitude of acceleration is $|a| = \omega^2 |x|$. At the extreme points $(x = \pm A)$,the displacement is maximum,so the acceleration is also maximum. Thus,statement $(D)$ is false.Therefore,statements $(A), (B),$ and $(C)$ are correct.

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