Which one of the following four particles, whose displacement x and ac

Which one of the following four particles, whose displacement x and acceleration a, are related as follows, is executing simple harmonic motion?

a = +3x

a = +3x²

a = -3

a = -3x

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC NDA-2 – 2016

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The particle executing simple harmonic motion is the one where acceleration ‘a’ and displacement ‘x’ are related as a = -3x.

Simple Harmonic Motion (SHM) is defined by a linear restoring force proportional to the displacement from the equilibrium position and directed towards it. According to Newton’s second law (F = ma), this implies that the acceleration is also proportional to the displacement and directed towards the equilibrium position. The general form of the acceleration-displacement relationship for SHM is a = -ω²x, where ω² is a positive constant (related to the system’s properties like mass and stiffness). Option D, a = -3x, fits this form with ω² = 3 (or ω = √3).

Option A, a = +3x, represents unstable equilibrium where the acceleration is away from the origin. Option B, a = +3x², is a non-linear relationship. Option C, a = -3, represents motion under constant acceleration, which is not SHM.

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