Question

In simple harmonic motion, the velocity is zero when:

• A. Displacement is zero
• B. Only displacement is maximum
• C. Only acceleration is maximum
• D. Both displacement and acceleration are maximum

Hint:

In simple harmonic motion, the velocity is zero at the extreme points of the oscillation, where the displacement and acceleration are maximum.

Answer 1

The Correct Option is D

In simple harmonic motion (SHM), the velocity of the oscillating object is given by \( v = \omega \sqrt{A^2 - x^2} \), where \( A \) is the amplitude of the motion, \( x \) is the displacement from the equilibrium position, and \( \omega \) is the angular frequency.
The velocity is zero when the displacement \( x \) is equal to the amplitude \( A \), i.e., at the maximum displacement. At this point, the object is momentarily at rest before reversing direction.
At this instant, the acceleration is also at its maximum because the acceleration in SHM is given by \( a = -\omega^2 x \), and when \( x = A \), the acceleration reaches its maximum value. Therefore, the correct condition is when both displacement and acceleration are at their maximum.
Thus, the velocity in simple harmonic motion is zero when both displacement and acceleration are maximum.