The distance moved by a particle in simple harmonic motion in one time period is

Options

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

Answer

To solve the problem of finding the distance moved by a particle in simple harmonic motion (SHM) in one complete time period, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion**:
- In SHM, a particle moves back and forth around an equilibrium position. The maximum displacement from this equilibrium position is called the amplitude (denoted as 'a').

2. **Movement in One Time Period**:
- One complete time period (T) consists of the particle moving from the equilibrium position to one extreme, back to the equilibrium position, to the opposite extreme, and then returning to the equilibrium position again.

3. **Path of the Particle**:
- Starting from the equilibrium position (0), the particle moves to the positive extreme position (a), then returns to the equilibrium position (0), moves to the negative extreme position (-a), and finally returns to the equilibrium position (0).

4. **Calculating the Distance**:
- The distance covered during each segment of the motion is as follows:
- From equilibrium (0) to positive extreme (a): distance = a
- From positive extreme (a) back to equilibrium (0): distance = a
- From equilibrium (0) to negative extreme (-a): distance = a
- From negative extreme (-a) back to equilibrium (0): distance = a
- Therefore, the total distance moved in one complete time period is:
\[ \text{Total Distance} = a + a + a + a = 4a \]

5. **Conclusion**:
- The distance moved by the particle in one time period is \( 4a \).

### Final Answer:
The distance moved by a particle in simple harmonic motion in one time period is \( 4a \).

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