In a SHM at extreme position the velocity becomes zero. Due to acceleration in opposite direction the velocity at extreme position becomes zero.

The maximum velocity of a particle in simple harmonic motion (SHM) is the highest velocity that the particle reaches during its motion. In this case, the maximum velocity is given as 2 cm/s.

To find the magnitude of the average velocity during one extreme position to another extreme position, we need to understand the nature of SHM and the relationship between velocity and displacement.

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from a fixed equilibrium position and acts in the opposite direction. The motion is characterized by a sinusoidal pattern.

In SHM, the particle oscillates back and forth around the equilibrium position. The extreme positions, also known as the turning points or the amplitude, are the points where the particle momentarily stops and changes direction.

The velocity of the particle is maximum at the equilibrium position, where the displacement is zero, and decreases as the particle moves away from the equilibrium position. At the extreme positions, the velocity is zero, as the particle momentarily stops before changing direction.

To find the magnitude of the average velocity during one extreme position to another extreme position, we need to consider the displacement of the particle during this interval.

The displacement of the particle from one extreme position to another extreme position is equal to twice the amplitude. Let's denote the amplitude as A.

Therefore, the displacement is given by:
Displacement = 2A

The average velocity is defined as the total displacement divided by the total time taken. In this case, the total time taken is the time taken for the particle to go from one extreme position to another extreme position and back.

The time taken for one complete cycle of SHM is known as the period, denoted by T. Therefore, the time taken for the particle to go from one extreme position to another extreme position and back is half of the period.

Therefore, the total time taken for this motion is given by:
Total time = T/2

Hence, the magnitude of the average velocity during one extreme position to another extreme position is:
Average velocity = Displacement / Total time
Average velocity = (2A) / (T/2)

This can be simplified as:
Average velocity = 4A / T

Since the period of SHM is related to the frequency, we can also express the average velocity in terms of the frequency (f) as:
Average velocity = 4A f

In conclusion, the magnitude of the average velocity during one extreme position to another extreme position in SHM is equal to 4 times the amplitude multiplied by the frequency.