The displacement of a particle undergoing S.H.M. as a function of time t is given by
`x = A sin((4pit)/(3))`
Where x is in cm and t in second
The time taken by the particle to travel from (a) x = 0 to A/2 is `t_(a)` and time taken by it to travel from (b) x = A/2 to A is `t_(b)`. Calculate the ratio `t_(b)//t_(a)`.

Explanation

To solve the problem, we need to find the ratio of the time taken by a particle undergoing simple harmonic motion (SHM) to travel from \( x = 0 \) to \( x = \frac{A}{2} \) (denoted as \( t_a \)) and from \( x = \frac{A}{2} \) to \( x = A \) (denoted as \( t_b \)).

### Step-by-Step Solution:

1. **Identify the equation of motion**:
The displacement of the particle is given by:
\[
x = A \sin\left(\frac{4\pi t}{3}\right)
...