Derivation for Problem in Tutorial 2B/2C

Here's the derivation for the equations for the problem I used in my tutorial videos. Specifically, it's the derivation for the problem used in Part 2B and Part 2C. I also decided to have Matlab integrate the nonlinear equations with ode45 to see how it compared to the linear approximation of those equations. The results turned out quite well! If you're interested, you'll find that part at 15:00.