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The restoring force in S.H.M. is directed
(A) always towards the extreme position
(B) always towards the mean position
(C) both a and b
(D) Neither a and b

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Last updated date: 17th Jun 2024
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Answer
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Hint: -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.
Imagine the following examples of simple harmonic motion to answer this question:
-The pendulum oscillating back and forth from the mean position.
-the vibration of a mass attached to a vertical spring,

Complete step by step answer
Simple harmonic motion can be described as an oscillatory motion in which the acceleration of the particle at any position is directly proportional to the displacement from the mean position. Mathematically this can be expressed as,
 $ F\propto -x\text{ } $ ….. (1)
 $ \text{a}\propto -x $
As given in expression (1) of restoring force of the S.H.M. , it is cleared that it is always produced in the opposite direction to the direction in which displacement occurs.
One can imagine the situation of the motion of a simple pendulum in which if the pendulum reaches the extreme position during one of the oscillations. Then, the restoring force is always acting towards the backward direction that is towards the mean position.
Therefore option (B) is correct.

Note
Restoring force: - It is a force which acts to bring a body to its equilibrium position. The restoring force is a function only of the position of the mass or particle, and it is always directed back toward the equilibrium position of the system.
Restoring force, F $ =- $ kx
The restoring force is mostly referred to in simple harmonic motion.