The relation between acceleration and displacement of four partical are given below
Which, one of the particle is exempting simple harmonic motion ?

Options

A. `a_(x)=+2_(x)`
B. `a_(x)=+2_(x)^(2)`
C. `a_(x)=-2_(x)^(2)`
D. `a_(x)=-2_(x)`

Explanation

To determine which particle is executing simple harmonic motion (SHM) based on the given relationships between acceleration and displacement, we need to analyze each relationship according to the standard form of SHM.

### Step-by-Step Solution:

1. **Understanding the Condition for SHM**:
- For a particle to be in SHM, the acceleration (A) must be directly proportional to the displacement (x) and must have a negative sign. The mathematical representation is:
\[
A = -\omega^2 x
...