A particle is executing simple harmonic motion. Which one of the follo

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A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true ?

It is always in the opposite direction to velocity
It is proportional to the frequency of oscillation
It is minimum when the speed is maximum
It decreases as the potential energy increases
This question was previously asked in
UPSC NDA-2 – 2016
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In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum.
Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -ω²x, where x is displacement and ω is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.
Option A is incorrect; acceleration is in the opposite direction to velocity only when the object is slowing down (moving away from equilibrium). When moving towards equilibrium, velocity and acceleration are in the same direction. Option B is incorrect; acceleration is proportional to the *square* of the angular frequency (ω²), not frequency directly, though frequency is proportional to ω. Option D is incorrect; potential energy is maximum at the extreme positions where |x| is maximum, and acceleration magnitude |a| = ω²|x| is also maximum there. So, as potential energy increases, acceleration magnitude increases, not decreases.

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