A particle is performing linear SHM, along x-axis when the displacement becomes, `(A)/(sqrt2)`, (A is the amplitude), the relation that holds between kinetic energy and potential energy is ……..

Explanation

To solve the problem, we need to find the relationship between the kinetic energy (KE) and potential energy (PE) of a particle performing simple harmonic motion (SHM) when its displacement from the mean position is \( \frac{A}{\sqrt{2}} \), where \( A \) is the amplitude.

### Step-by-Step Solution:

1. **Understanding SHM**:
In simple harmonic motion, the total mechanical energy (E) is conserved and is the sum of kinetic energy and potential energy. The potential energy (PE) at a displacement \( x \) from the mean position is given by:
\[
PE = \frac{1}{2} k x^2
...