The displacement of a harmonic oscillator is half of its amplitude. What fraction of the total energy is kinetic and what fraction is potential ?

Explanation

To solve the problem, we need to determine the fractions of kinetic and potential energy when the displacement of a harmonic oscillator is half of its amplitude. Here’s a step-by-step breakdown:

### Step 1: Define the Variables
Let:
- \( A \) = Amplitude of the harmonic oscillator
- \( x \) = Displacement from the mean position = \( \frac{A}{2} \)

### Step 2: Calculate Total Energy
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