The acceleration of a particle moving along x-axis is `a=-100x+50`. It is released from `x=2`. Here `a` and `x` are in S.I units. The motion of particle will be:

Options

A. periodic, oscillatory but not SHM.
B. periodic but not oscillatory
C. oscillatory but not periodic.
D. simple harmonic.

Explanation

To solve the problem, we need to analyze the given acceleration equation and determine the nature of the motion of the particle.

### Step-by-Step Solution:

1. **Identify the given acceleration equation**:
The acceleration of the particle is given by:
\[ a = -100x + 50 \]

2. **Rearrange the equation**:
We can rearrange the equation to isolate the terms related to \(x\):
\[ a + 100x = 50 \]
or
\[ a = -100x + 50 \]

3. **Identify the form of the equation**:
The equation can be rewritten as:
\[ a = -100x + 50 \]
This shows that the acceleration \(a\) is a linear function of displacement \(x\).

4. **Determine the nature of the motion**:
In simple harmonic motion (SHM), the acceleration is directly proportional to the negative of the displacement from the equilibrium position. The general form for SHM is:
\[ a = -kx \]
where \(k\) is a positive constant.

5. **Analyze the constant term**:
The presence of the constant term (+50) indicates that the system has a force acting on it that is not dependent on the displacement \(x\). This means that the particle is not oscillating around the equilibrium position at \(x=0\) but rather around a shifted equilibrium position.

6. **Determine the equilibrium position**:
To find the equilibrium position, we set the acceleration to zero:
\[ 0 = -100x + 50 \]
Solving for \(x\):
\[ 100x = 50 \implies x = 0.5 \]
This means the particle will oscillate around \(x = 0.5\).

7. **Conclusion**:
Since the acceleration is proportional to the negative of the displacement from the equilibrium position, the motion of the particle is indeed simple harmonic motion (SHM).

### Final Answer:
The motion of the particle will be **Simple Harmonic Motion (SHM)**.