Question

For a particle executing simple harmonic motion , which of the following statements is NOT correct?

• A. The magnitude of acceleration is directly proportional to displacement.
• B. The restoring force is always directed towards fixed point.
• C. The restoring force is maximum at extreme position.
• D. The acceleration of the particle is maximum at equilibrium position.

Hint:

In S.H.M. the acceleration is proportional to displacement, so it is zero at the mean position and maximum at the extremes.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In S.H.M., \(a=-\omega^{2}x\) and the restoring force is \(F=-kx\). Both are proportional to the displacement and point towards the mean position.

Step 2: Check each statement
The first is true because \(|a|\propto|x|\). The second is true because the force always points towards the fixed point. The third is true because \(x\) is largest at the extremes, so the force is largest there.

Step 3: Find the false one
At the equilibrium position \(x=0\), so the acceleration is zero, not maximum. The last statement is incorrect.

Final Answer:
The statement that acceleration is maximum at the equilibrium position is not correct. \[ \boxed{\text{(D) }\text{The acceleration of the particle is maximum at equilibrium position}} \]