Question

For a particle executing simple harmonic motion, the restoring force is proportional to:

• A. Velocity of the particle
• B. Square of displacement
• C. Displacement from mean position
• D. Acceleration of the particle

Hint:

Always remember the "linear" nature of SHM.
Restoring Force \(\propto -x\) and Acceleration \(\propto -x\).
If the force were proportional to \( x^2 \), the motion would be periodic but not "Simple Harmonic".

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Simple Harmonic Motion (SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.
Step 2: Key Formula or Approach:
The mathematical expression for the restoring force \( F \) in SHM is given by Hooke's Law:
\[ F = -k x \]
Where:
\( k \) is the force constant (or spring constant).
\( x \) is the displacement of the particle from its mean (equilibrium) position.
The negative sign indicates that the force is always directed opposite to the displacement.
Step 3: Detailed Explanation:
In SHM, as the particle moves away from the mean position, the restoring force increases linearly with the distance \( x \).
If we double the displacement, the restoring force required to bring the particle back to the center also doubles.
Option (A) is incorrect because the force is related to acceleration, not directly to velocity.
Option (B) describes a non-linear relationship which does not characterize SHM.
Option (D) is related because \( F = ma \), so acceleration is also proportional to displacement, but the fundamental definition of the "restoring force" is based on the displacement itself.
Step 4: Final Answer:
Thus, the restoring force is proportional to the displacement from the mean position.