Which of the following is not characteristics of simple harmonic motion?

Options

A. The motion is periodic
B. the motion is along a straight line about the mean position
C. The oscillations are responsible for the energy conversion.
D. The acceleration of the particle is directed towards the extreme position.

Explanation

To determine which of the given options is not a characteristic of simple harmonic motion (SHM), we will analyze each option step by step.

### Step 1: Analyze Each Option

1. **First Option: The motion is periodic.**
- Simple harmonic motion is indeed periodic, meaning it repeats itself after a certain time interval. Therefore, this option is a characteristic of SHM.

2. **Second Option: The motion is along a straight line about the mean position.**
- In SHM, the motion occurs along a straight line (or a single axis) around a central point known as the mean position. This is also a characteristic of SHM.

3. **Third Option: The oscillations are responsible for energy conservation.**
- In SHM, energy is conserved as it oscillates between kinetic and potential forms. The total mechanical energy remains constant. Thus, this option is also a characteristic of SHM.

4. **Fourth Option: The acceleration of the particle is directed towards the extreme position.**
- This statement is incorrect. In SHM, the acceleration of the particle is directed towards the mean position, not the extreme position. Therefore, this option is not a characteristic of SHM.

### Conclusion
The option that is **not a characteristic of simple harmonic motion** is the **fourth option**: "The acceleration of the particle is directed towards the extreme position."

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