Question

For a particle executing simple harmonic motion (SHM), at its mean position

• A. Velocity is zero and acceleration is maximum
• B. Velocity is maximum and acceleration is zero
• C. Both velocity and acceleration are maximum
• D. Both velocity and acceleration are zero

Answer 1

The Correct Option is B

For a particle executing simple harmonic motion (SHM), let's analyze the situation at the mean position (equilibrium point).

At the Mean Position:

• Velocity: The velocity is maximum at the mean position because the particle passes through the equilibrium point and the restoring force is zero. This gives the maximum kinetic energy and the particle moves the fastest.
• Acceleration: The displacement from the mean position is zero, so the restoring force is zero, and hence the acceleration is also zero. Since acceleration is proportional to displacement (\( a = -\omega^2 x \)), at \( x = 0 \), acceleration is zero.

The correct answer is (B) Velocity is maximum and acceleration is zero.

Answer 2

In simple harmonic motion (SHM), at the mean position (x = 0), the velocity is at its maximum and the acceleration is zero. The equations for SHM are: \[ V = \omega A \sqrt{1 - (x/A)^2} \] \[ a = -\omega^2 x \] At the mean position, x = 0, so acceleration (a) is zero and velocity is at maximum.