Chapter 5.1, Problem 1E

Interpretation Introduction

Interpretation:

The orbits of the system of the harmonic oscillator $\dot{\text{x}}\text{ = v}$, ${\dot{\text{v}}\text{ = -ω}}^{\text{2}}\text{x}$ are given by ellipses ${\text{ω}}^{\text{2}}{\text{x}}^{\text{2}}{\text{ + v}}^{\text{2}}\text{ = C}$ and this condition is equivalent to the conservation of energy is to be proved.

Concept Introduction:

Harmonic oscillator undergoes periodic motion.

The energy is conserved for the harmonic oscillator.

$\text{PE + KE = constant}$