The average displacement over a period of SHM is ____ (A = amplitude of SHM )

Options

A. 0
B. A
C. 2A
D. 4A

Explanation

To solve the question regarding the average displacement over a period of Simple Harmonic Motion (SHM), let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding SHM**:
- In Simple Harmonic Motion, an object oscillates back and forth around a central position (mean position). The maximum distance from this mean position is called the amplitude (A).

2. **Definition of Displacement**:
- Displacement is defined as the change in position of an object. It is a vector quantity that considers the initial and final positions of the object.

3. **Analyzing One Complete Cycle**:
- In one complete cycle of SHM, the object moves from the mean position to one extreme position (A), back to the mean position, then to the opposite extreme position (-A), and finally returns to the mean position.

4. **Calculating Average Displacement**:
- Average displacement over a complete cycle is calculated as:
\[ \text{Average Displacement} = \frac{\text{Total Displacement}}{\text{Time Period}} \]
- Since the object returns to its starting position (the mean position) after one complete cycle, the total displacement is zero.

5. **Conclusion**:
- Therefore, the average displacement over a period of SHM is:
\[ \text{Average Displacement} = 0 \]

### Final Answer:
The average displacement over a period of SHM is **0**.

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