Question

In simple harmonic motion (SHM), the force acting on the particle is:

• A. Proportional to the square of displacement
• B. Inversely proportional to displacement
• C. Proportional to the cube of displacement
• D. Proportional to the displacement and in the opposite direction

Hint:

In SHM, always remember: \( F = -kx \). The force is linear with displacement and acts to restore equilibrium, hence the negative sign.

Answer 1

The Correct Option is D

Step 1: In simple harmonic motion (SHM), the defining characteristic is that the restoring force acting on the particle is directly proportional to the displacement from the mean position and acts in the direction opposite to the displacement.
Step 2: Mathematically, this is expressed as: \[ F = -kx \] where \( F \) is the restoring force, \( k \) is a constant (spring constant or force constant), and \( x \) is the displacement. The negative sign indicates the force acts in the opposite direction to the displacement.
Step 3: This linear relationship between force and displacement is what leads to sinusoidal motion, distinguishing SHM from other types of oscillations.
Why the other options are incorrect:

• (A) Square of displacement implies a nonlinear restoring force—not SHM.
• (B) Inverse proportionality is not characteristic of SHM.
• (C) Cube of displacement again suggests a nonlinear system.