A particle startsits SHM at `t=0` . At a particular instant on its way to extreme position , `x= (A)/(2)` . Find the time taken by the particle to come back to this point after passing through the extreme position.
Hint `: t_(1) = ` time taken to go from `x=0` to `x= (A)/(2)`
`t_(2) =` time taken to go to extreme position and come back to mean position `= (T)/(2)`
Required time `= (T)/(2) - t_(1)`

Explanation

To solve the problem, we need to find the time taken by a particle undergoing simple harmonic motion (SHM) to return to the position \( x = \frac{A}{2} \) after it has passed through the extreme position \( x = A \).

### Step-by-Step Solution:

1. **Understanding the Motion**:
The particle starts at \( x = 0 \) (the mean position) at \( t = 0 \) and moves towards the extreme position \( x = A \). At some time \( t_1 \), it reaches the position \( x = \frac{A}{2} \).

2. **Finding \( t_1 \)**:
...