In simple harmonic motion,the particle is

Options

A. always acceleration
B. always retarded
C. alternately acceleration and retarded
D. neither acceleration nor retarded

Explanation

To solve the question regarding the behavior of a particle in simple harmonic motion (SHM), we will analyze the acceleration of the particle at different positions.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- In SHM, a particle oscillates around a mean position (equilibrium position). The motion is periodic, and the particle moves back and forth.

2. **Acceleration in SHM**:
- The acceleration \( a \) of a particle in SHM is given by the formula:
\[ a = -\omega^2 x \]
- Here, \( \omega \) is the angular frequency, and \( x \) is the displacement from the mean position.

3. **Analyzing Acceleration**:
- At the mean position (\( x = 0 \)):
\[ a = -\omega^2 \cdot 0 = 0 \]
- At the extreme positions (\( x = +a \) or \( x = -a \)):
\[ a = -\omega^2 a \quad \text{(maximum magnitude)} \]
- The direction of acceleration is always towards the mean position.

4. **Behavior of the Particle**:
- When the particle is moving towards the mean position, it is **accelerated** because the acceleration is directed towards the mean position.
- When the particle is moving away from the mean position, it is **retarded** because the acceleration acts in the opposite direction to its motion.

5. **Conclusion**:
- As the particle oscillates, it alternates between being accelerated (when moving towards the mean position) and retarded (when moving away from the mean position).
- Therefore, the correct answer is that the particle is **alternatively accelerated and retarded**.

### Final Answer:
The correct option is **alternatively accelerated and retarded**.

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