For a particle executing simple harmonic motion, the acceleration is -

Options

A. is uniform
B. varies linearly with time
C. is non-uniform
D. Both (b) and (c)

Explanation

To solve the question regarding the acceleration of a particle executing simple harmonic motion (SHM), we will analyze the relationship between acceleration, displacement, and time.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- In SHM, a particle oscillates about a mean position. The key characteristics of SHM include periodic motion and a restoring force that is proportional to the displacement from the mean position.

2. **Acceleration in SHM**:
- 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. **Analyzing the Formula**:
- The negative sign indicates that the acceleration is directed towards the mean position (restoring force).
- The acceleration depends on the displacement \( x \). As \( x \) changes, \( a \) also changes.

4. **Uniform vs. Non-Uniform Acceleration**:
- **Uniform Acceleration**: This would mean that the acceleration remains constant over time, which is not the case here since \( a \) varies with \( x \).
- **Non-Uniform Acceleration**: Since \( a \) changes with \( x \) (and thus changes as the particle moves), the acceleration is non-uniform.

5. **Time Dependency**:
- The formula \( a = -\omega^2 x \) shows that acceleration does not depend on time directly. It varies with displacement, not time.

6. **Conclusion**:
- Based on the analysis, the correct answer is that the acceleration is **non-uniform** since it varies with displacement from the mean position. The other options (uniform, varies linearly with time) are incorrect.

### Final Answer:
The acceleration of a particle executing simple harmonic motion is **non-uniform**.

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