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I finally got around to finishing the all the "subsections" of Part 2 of this tutorial. I didn't originally intend to make this video, but I was encouraged to do so after being asked about a faster way to put equations in state space form. This video shows an easy way to take physical, linear MDOF systems and put them in state space format using matrix equations. Be warned that in addition to requiring a linear system, this method assumes that the mass matrix is invertible. This method is not restricted to physical systems, but may be applied to any linear system of 2nd order ordinary differential equations (where the 2nd-order derivative matrix is invertible). Hope this helps!
As a warning to ME students attending UMCP and submitting ode45 assignments to Professor Nguyen: Don't think he won't expect you to understand and explain how this process works if you use it. If you use this on any of his assignments, I strongly recommend studying the derivation for this state space set-up.
Textbook:
Vibrations, Second Edition by Balakumar Balachandran and Edward B. Magrab
I want to give my sincerest thanks to the legendary Professor Vincent Nguyen at the University of Maryland, College Park. Without his help, I would never be able to understand how to use Matlab's ode solver like I do today.