Question

In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given below:

• A. (A), (B) and (C) Only
• B. (C) and (D) only
• C. (A), (C) and (D) only
• D. A), (B) and (D) only

Hint:

In Simple Harmonic Motion, recall that acceleration is maximum at the extreme points and velocity is maximum at the mean position.

Answer 1

The Correct Option is A

In this question, we are asked to evaluate various statements about linear Simple Harmonic Motion (SHM) and select the correct combination from the options provided. Let’s analyze each statement to identify the correct ones:

1. (A) Restoring force is directly proportional to the displacement: This statement is true. In SHM, the restoring force F is given by F = -kx, where k is the force constant and x is the displacement from the mean position. This relation confirms that the restoring force is directly proportional to the displacement.
2. (B) The acceleration and displacement are opposite in direction: This statement is also true. The acceleration a in SHM is given by a = -\omega^2 x, where \omega is the angular frequency and x is the displacement. This negative sign indicates that the acceleration is always opposite to the displacement.
3. (C) The velocity is maximum at the mean position: This statement is true. In SHM, the velocity is maximum when the object passes through the mean position because all the potential energy is converted into kinetic energy at this point.
4. (D) The acceleration is minimum at extreme points: This statement is false. At the extreme points, the magnitude of acceleration is actually maximum because the displacement from the mean position is greatest.

Based on our analysis, statements (A), (B), and (C) are correct. Hence, the correct answer is (A), (B) and (C) Only.