The displacement of a particle in simple harmonic motion in one time period is

Options

A. A
B. 2A
C. 4A
D. zero

Answer

To solve the question regarding the displacement of a particle in simple harmonic motion (SHM) over one complete time period, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- In SHM, a particle moves back and forth around an equilibrium position. The motion is periodic, meaning it repeats itself after a certain time interval known as the time period (T).

2. **Identifying the Time Period**:
- The time period (T) is the time taken for the particle to complete one full cycle of motion. In one time period, the particle will return to its starting position.

3. **Analyzing the Motion**:
- Let's assume the particle starts at position A (the equilibrium position). As it moves, it will reach the maximum displacement (amplitude) on one side, then return through the equilibrium position to the maximum displacement on the opposite side, and finally return to position A.

4. **Determining Initial and Final Positions**:
- At the start of the time period (t = 0), the particle is at position A. After one complete time period (t = T), the particle returns to position A.

5. **Calculating Displacement**:
- Displacement is defined as the change in position of the particle, which is the difference between the final position and the initial position.
- Since the initial position (A) and final position (A) are the same after one complete cycle, the displacement can be calculated as:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = A - A = 0 \]

6. **Conclusion**:
- Therefore, the displacement of the particle in simple harmonic motion over one time period is zero.

### Final Answer:
The displacement of a particle in simple harmonic motion in one time period is **zero**.

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