Using GNU Octave to numerically find a solution for a system of harmonic oscillators
Channel: jason thomas
Date: 25/06/2023

_Notes:_ 
- At 1:25, I say that the governing equation for a pendulum is a simple harmonic oscillator. This is only true at small angles.
- The metronomes are similar but not entirely analogous. Sometimes metronomes end up in anti-phase sync.
- This video is the sum of my understanding as an undergraduate, so I might have gotten a detail or two wrong. Please comment if you can see any issues.

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I talk about how I use GNU Octave to find approximate solutions to systems of differential equations by using numerical techniques.

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*Links to elsewhere*

- Deriving the second order DE of a single pendulum: Physics with Elliot, https://www.youtube.com/watch?v=0q0L7Fj4dk8

- Choosing an ODE solver: Matlab documentation, https://au.mathworks.com/help/matlab/math/choose-an-ode-solver.html

- Setting up Gnu Octave to run with Jupyter Notebook, https://www.jason-thomas.xyz/post?postNum=20

- The video script, code to find solutions, and all files used to make the video,  https://github.com/JasonThomasData/mathsVideos/blob/master/GnuOctaveNumericalSolutions/script%20and%20code.ipynb

- Install the OCL package, https://gnu-octave.github.io/packages/ocl/

- Video sample of metronomes in-phase sync, https://www.youtube.com/watch?v=8VNzffu914A