Displacement between max. P.E. position and max. K.E. position for a particle excuting simple harmonic motion is : -

Options

A. `pma/2`
B. `+a`
C. `pma`
D. `-1`

Explanation

To find the displacement between the maximum potential energy (P.E.) position and the maximum kinetic energy (K.E.) position for a particle executing simple harmonic motion (SHM), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Positions in SHM**:
- In simple harmonic motion, the particle oscillates between two extreme positions, known as the amplitude (A) and -A. The midpoint of this motion is considered the equilibrium position.

2. **Identify Maximum Kinetic Energy Position**:
- The maximum kinetic energy occurs at the equilibrium position (midpoint) where the displacement (y) is 0. At this point, the particle is moving fastest.

3. **Identify Maximum Potential Energy Position**:
- The maximum potential energy occurs at the extreme positions, which are at +A and -A. At these points, the particle momentarily comes to rest before changing direction.

4. **Calculate Displacement**:
- The displacement between the maximum potential energy position (either +A or -A) and the maximum kinetic energy position (0) can be calculated as follows:
- From +A to 0: Displacement = 0 - A = -A
- From -A to 0: Displacement = 0 - (-A) = A

5. **Conclusion**:
- The displacement between the maximum potential energy position and the maximum kinetic energy position is A (from -A to 0) or -A (from +A to 0). Therefore, the absolute displacement is A.

### Final Answer:
The displacement between the maximum potential energy position and the maximum kinetic energy position for a particle executing simple harmonic motion is A.