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

Answer

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. **Understand the Given Information:**
The acceleration of the particle is given by the equation:
\[ a = -100x + 50 \]
The particle is released from the position \( x = 2 \).

2. **Rearranging the Acceleration Equation:**
We can rearrange the acceleration equation to isolate the terms involving \( x \):
\[ a - 50 = -100x \]
This can be rewritten as:
\[ a = -100x + 50 \]

3. **Analyzing the Form of the Acceleration:**
The equation can be expressed as:
\[ a = -100x + 50 \]
This indicates that the acceleration \( a \) depends linearly on the position \( x \).

4. **Identifying the Characteristics of Motion:**
The acceleration is proportional to the negative of the displacement \( x \) (after rearranging), which suggests that the particle experiences a restoring force towards a fixed point. This is a characteristic of Simple Harmonic Motion (SHM).

5. **Criteria for Simple Harmonic Motion:**
For a motion to be classified as SHM, the following conditions must be satisfied:
- The acceleration must be directly proportional to the displacement from an equilibrium position.
- The acceleration must always act towards the equilibrium position.

6. **Conclusion:**
Since the acceleration \( a \) can be expressed as:
\[ a = -100x + 50 \]
and the term \(-100x\) indicates that the acceleration is directed towards the origin (or a fixed point), we conclude that the motion of the particle is indeed Simple Harmonic Motion (SHM).

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