Please find attached the 'Report' file containing the work. The Python code used to plot phase diagram of the harmonic oscillator can be found in the appendix.
Abstract: I was extremely intrigued by phase space trajectories when I encountered them. Having seen a few phase space diagrams in the lecture notes, I decided to code and plot phase space trajectories of some simple systems myself. In this very brief self-study, I recap the basics of Hamiltonian dynamics and then plot phase space portraits of simple, 1 degree of freedom, autonomous systems using the lecture notes as my primary resource. I discuss how phase diagrams can be such a powerful tool to study the dynamics of a system.
If you need more information related to the work, don't hesitate to contact me.