The acceleration of a particle in SHM is:

Options

A. always zero
B. always constant
C. maximum at mean position
D. maximum at amplitude

Answer

To find the acceleration of a particle in Simple Harmonic Motion (SHM), we start with the fundamental relationship that defines acceleration in SHM.

### Step-by-Step Solution:

1. **Understanding SHM**:
Simple Harmonic Motion is characterized by a restoring force that is proportional to the displacement from the mean position and acts in the opposite direction.

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

3. **Magnitude of Acceleration**:
The magnitude of the acceleration can be expressed as:
\[ |a| = \omega^2 |x| \]

4. **Displacement \( x \)**:
In this context, \( x \) represents the displacement of the particle from its equilibrium (mean) position.

5. **Analyzing Options**:
- **Option 1**: Always 0 - This is incorrect because the acceleration is only zero when the particle is at the mean position (where \( x = 0 \)).
- **Option 2**: Always constant - This is also incorrect because the displacement \( x \) changes as the particle moves, thus the acceleration changes.
- **Option 3**: Maximum at mean position - This is incorrect since the acceleration is zero at the mean position.
- **Option 4**: Maximum at amplitude - This is correct because at maximum displacement (amplitude \( A \)), \( x = \pm A \), leading to maximum acceleration \( |a| = \omega^2 A \).

6. **Conclusion**:
Therefore, the correct statement regarding the acceleration of a particle in SHM is that it is maximum at the amplitude.

### Final Answer:
The acceleration of a particle in SHM is maximum at the amplitude.