The shortest distance travelled by a particle executing S.H.M. from mean position in 4 seconds is eual to `(1)/(sqrt(2))` times its amplitude. Find the time period.
Hint `: t=4 s , x = (1)/(sqrt(2)) , T=?`
`x = A sin omega t , omega = ( 2pi)/( T )`
Solve to get T.

Explanation

To solve the problem, we will follow the steps outlined in the video transcript and use the relevant equations for Simple Harmonic Motion (SHM).

### Step-by-Step Solution:

1. **Understanding the Problem**:
We are given that the shortest distance traveled by a particle executing SHM from the mean position in 4 seconds is equal to \( \frac{1}{\sqrt{2}} \) times its amplitude \( A \). We need to find the time period \( T \).

2. **Identify Given Values**:
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