For a particle undergoing simple harmonic motion (SHM), the velocity attains maximum magnitude at two points in its motion: the equilibrium position (mean position) and the extreme positions.
Equilibrium Position: At the equilibrium position, the particle momentarily stops and changes direction. Since the particle is momentarily at rest, its velocity is zero, and the magnitude of the velocity is at a maximum. This occurs when the particle crosses the mean position while oscillating back and forth.
Extreme Positions: At the extreme positions of the motion, where the displacement from the mean position is maximum, the particle also attains its maximum velocity. However, the direction of the velocity at the extreme positions is opposite to the direction at the equilibrium position. The magnitude of the velocity is again at a maximum, but this time the particle is moving at its maximum speed.
The velocity attains its minimum magnitude at the mean position (equilibrium position) and the extreme positions. At these points, the particle momentarily comes to a halt, and its velocity is zero. However, it should be noted that the minimum magnitude of velocity does not mean that the particle has no velocity throughout the entire SHM cycle. It simply means that the velocity momentarily drops to zero before changing direction.
In summary:
- Maximum magnitude of velocity: Equilibrium position and extreme positions.
- Minimum magnitude of velocity: Equilibrium position and extreme positions.