The speed `v` of particle moving along x-axis is given by `v^(2) = 8bx - x^(2) - 12 b^(2)`, where 'b' is a constant. Find amplitude, maximum velocity and time period of oscillation.

Explanation

To solve the problem step-by-step, we will analyze the given equation for velocity and derive the amplitude, maximum velocity, and time period of oscillation.

### Step 1: Understand the given equation
The equation for the speed \( v \) of a particle moving along the x-axis is given by:
\[ v^2 = 8bx - x^2 - 12b^2 \]
where \( b \) is a constant.
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