Average velocity of a particle executing SHM in one complete vibration is :

Options

A. zero
B. `(Aomega)/(2)`
C. `Aomega`
D. `(Aomega^(2))/(2)`

Explanation

To find the average velocity of a particle executing Simple Harmonic Motion (SHM) in one complete vibration, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding SHM**: A particle in SHM moves back and forth around an equilibrium position. In one complete vibration, the particle moves from one extreme position to the other and then returns to the starting point.

2. **Displacement Calculation**: Displacement is defined as the change in position of the particle. In one complete vibration, the particle starts from an extreme position, moves to the opposite extreme, and then returns to the original position. Therefore, the initial and final positions are the same.

3. **Displacement Value**: Since the particle returns to its starting point after one complete vibration, the total displacement is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 - 0 = 0 \]

4. **Time Calculation**: Let \( T \) be the time taken for one complete vibration (one complete oscillation).

5. **Average Velocity Formula**: Average velocity is defined as:
\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{0}{T} = 0 \]

6. **Conclusion**: Therefore, the average velocity of a particle executing SHM in one complete vibration is:
\[ \text{Average Velocity} = 0 \]

### Final Answer:
The average velocity of a particle executing SHM in one complete vibration is **0**.