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  4. Assertion: In simple harmonic motion, the motion is to and fro and periodic. Reason: Velocity of the particle (v) = ω√k2-x2 (where x is the displacement).

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

AIIMSAIIMS 2002Oscillations

Solution:

A particle is said to execute simple harmonic motion, if it moves to and fro about a fixed point under the action of a restoring force which is directly proportional to its displacement from the fixed point and is always directed towards the fixed point. Also the velocity of the particle when its displacement is
$x, v=\omega\sqrt{k^{2}-x^{2}}$.