Which one of the following statements is true for a simple harmonic os

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Which one of the following statements is true for a simple harmonic oscillator ?

Force acting is directly proportional to the displacement from the mean position and is in same direction.
Force acting is directly proportional to the displacement from the mean position and is in opposite direction.
Acceleration of the oscillator is constant.
The velocity of the oscillator is not periodic.
This question was previously asked in
UPSC NDA-1 – 2021
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The correct answer is (B) Force acting is directly proportional to the displacement from the mean position and is in opposite direction.
A simple harmonic oscillator (SHO) is defined by the condition that the restoring force acting on the oscillating body is directly proportional to its displacement from the equilibrium (mean) position and is always directed towards the equilibrium position. This is mathematically represented as F = -kx, where F is the force, x is the displacement, and k is the force constant. The negative sign indicates the force is in the opposite direction to the displacement.
Option A is incorrect because the force is in the opposite direction to the displacement (restoring force). Option C is incorrect because the acceleration (a = F/m = -kx/m) is proportional to the displacement and thus varies; it is not constant. Option D is incorrect because in SHM, the motion is periodic, meaning all properties like velocity, displacement, and acceleration repeat over time.

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