Question

Draw a labelled diagram of the phase space
for a linear harmonic oscillator.

Answer 1

The total energy of a linear harmonic oscillator

$$E=\frac{p^2}{2m}+\frac{m\omega^2 x^2}{2}=const$$

The phase trajectory equation

$$\frac{p^2}{(\sqrt{2mE})^2}+\frac{x^2}{(\sqrt{2E/m\omega^2})^2}=1$$