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 oscillates about an equilibrium position. It moves to a maximum displacement (amplitude) on one side, returns to the equilibrium position, moves to the maximum displacement on the opposite side, and then returns to the equilibrium position again.

2. **Displacement in One Complete Cycle**:
- In one complete vibration (or cycle), the particle starts from the equilibrium position, moves to the maximum positive displacement (amplitude), returns to the equilibrium position, moves to the maximum negative displacement, and finally returns to the equilibrium position.
- The total displacement after one complete cycle is zero because the particle ends up where it started.

3. **Average Velocity Formula**:
- Average velocity (V_avg) is defined as the total displacement divided by the total time taken for that displacement:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

4. **Calculating Average Velocity**:
- Since the total displacement for one complete cycle is zero, we can substitute this into the average velocity formula:
\[ V_{avg} = \frac{0}{T} = 0 \]
- Here, T is the total time taken for one complete vibration.

5. **Conclusion**:
- Therefore, the average velocity of a particle executing SHM in one complete vibration is **0**.

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