I am currently studying a few math systems which use compiled code and are powerful enough to do real math. Along the way I came across the very nice Python approach named SciPy. I did not try the code, but I certainly will.
Along the way I found an example on their pages, where they compute a mass system with two masses and a spring.
(Image from the PySci page)
There is a glitch in the code, which effectively sets m2=1, though they want m2=1.5, which would cause x1 to become negative. I could not mail anybody this tiny error. There is only a mailing list, and I do not want to sign up just for this report.
I tried to get the video off the screen using Microsoft Expression Encoder 4 Screen Capture. But it is tough to start the animation and the video at the same time. Here is my not so successful attempt.