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Solution of the nonlinear equation
   • MM61: Simple pendulum and elliptic integrals  
   • Exact Solution of the Nonlinear Pendulum [...  
   • Pillai "Simple Pendulum and Elliptic Integ...  

sin and co form a circle
   • Sine and cosine from rotating vector  

Walter Lewin talking about SHM equation (at min 8)
   • 8.01x - Lect 10 - Hooke's Law, Springs, Pe...  

Code to plot the linear vs nonlinear equations
   • Coding a Numerical Solution to the Simple ...  

The original code I used in my demo
https://github.com/nature-of-code/noc...
This code is for one pendulum with nonlinear acceleration, but could be easily modified to add another pendulum with linear acceleration with the position.