When the displacement is one half of the amplitude, what fraction is potential in SHM ? At what displacement is the energy half kinetic and half potential?

Explanation

To solve the problem, we will break it down into two parts as per the question.

### Part 1: Finding the fraction of potential energy when displacement is one half of the amplitude.

1. **Understanding the formulas**:
- The potential energy (PE) in Simple Harmonic Motion (SHM) is given by:
\[
PE = \frac{1}{2} m \omega^2 y^2
...