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:

Solution

Physics sir · 2 steps

Everything in SHM follows from one line, a = -ω² x: check each statement against it.

1. Start from the definition. Linear SHM means the restoring force is F = -kx. Dividing by mass gives the acceleration, and the velocity follows from energy.

   a = -ω² x, v = ω√(A² - x²)

   Statement	Check with the equations	Verdict
   (A) Force proportional to displacement	|F| = k|x|	True
   (B) Acceleration opposite to displacement	The minus sign in a = -ω² x	True
   (C) Velocity maximum at mean position	At x = 0, v = ω A, the largest value	True
   (D) Acceleration minimum at extremes	At x = ± A, |a| = ω² A, the largest value	False

2. So. (A), (B) and (C) are correct and (D) is wrong, which is option (c).

The idea to keep. In SHM, speed and acceleration swap roles: speed is largest at the mean position and zero at the extremes, while acceleration is zero at the mean position and largest at the extremes.

Answer from the NTA final answer key. Solution by PrepWiser.