At what displacement is the velocity of the body executing SHM is half of that at the mean position?

CONCEPT:

• Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position.
  • The direction of this restoring force is always towards the mean position.
• Amplitude: It is the maximum displacement of the particle.
• Time period: The minimum time after which the particle keeps on repeating its motion is known as the time period.

CALCULATION:

At the mean position,

⇒ v = Aω     -----(1)

• Velocity at half the amplitude is,

For,

Hence, option 3 is correct.

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