Assertion : In simple harmonic motion,the mot | vedclass

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(A) Simple Harmonic Motion $(SHM)$ is defined as a periodic motion in which the restoring force is directly proportional to the displacement and acts

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If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

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(A) Simple Harmonic Motion $(SHM)$ is defined as a periodic motion in which the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This results in to-and-fro motion about a mean position. The velocity of a particle in $SHM$ is given by the formula $v = \omega \sqrt{A^2 - x^2}$,where $A$ is the amplitude,$x$ is the displacement,and $\omega$ is the angular frequency. The original reason provided used $k$ instead of $A$,which is notationally incorrect for amplitude. However,the formula correctly describes the velocity variation in $SHM$,which confirms the periodic and to-and-fro nature of the motion. Thus,both statements are correct,and the velocity expression explains the nature of the motion.

$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic.
$Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).

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$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic. $Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).