A particle constrained to move along x-axis given a velocity u along the positive x-axis. The acceleration ' a ' of the particle varies as a = - bx, where b is a positive constant and x is the x co-ordinate of the position of the particle . Then select the correct alternative(s): .

Options

A. The maximum displacement of the particle from the starting point is `u/(sqrt(b))`
B. The particle will oscillate about the origin
C. Velocity is maximum at the origin
D. Given data is insufficient to determine the exact motion of the particle.

Explanation

To solve the problem, we need to analyze the motion of a particle constrained to move along the x-axis with a given velocity and a specific form of acceleration. The acceleration is given as \( a = -bx \), where \( b \) is a positive constant and \( x \) is the position of the particle.

### Step-by-Step Solution:

1. **Understand the Acceleration**:
The acceleration of the particle is given by the equation \( a = -bx \). This indicates that the acceleration is proportional to the negative of the position \( x \). This is characteristic of simple harmonic motion (SHM).

2. **Relate Acceleration to Velocity**:
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