State the expression for the total energy of a particle performing linear SHM. What conclusions can be drawn from the expression for the total energy ?

Explanation

To find the expression for the total energy of a particle performing linear simple harmonic motion (SHM), we start with the definitions of kinetic energy (KE) and potential energy (PE) in the context of SHM.

### Step-by-Step Solution:

1. **Define Potential Energy (PE)**:
The potential energy of a particle in SHM at a displacement \( x \) from the mean position is given by:
\[
PE = \frac{1}{2} k x^2
...