So as part of my clavichord build, I’m trying to simulate the vibrations that happen within the instrument when a string is struck.
To do that, I’m building up a physical simulation from scratch. Over the last two days, I’ve gone from a 1-dimensional mass-spring simulation to a 2D one.
Yesterday’s work was to extend the math of the 1D version to handle 2D. Today’s work was to make sure that multiple nodes could be handled in a realistic fashion.
The hardest part for me so far was to figure out how to apply forces in defined directions in a realistically proportionate way. The example I read first (here) did not bother doing this, so the physics was incorrect.
Luckily, I remembered some trigonometry and was able to use Pythagoras’s theorem and some SOHCAHTOA usage to figure it out.
Springs in real life don’t just bounce for ever, so I applied some damping to the springs based on some example math I found based on Hooke’s spring law:
Relative velocity (va-vb in the above) was found by measuring the distance between the end points, measuring the distance between the end points after velocity in all dimensions are added, then simply subtracting one from the other
The end result is pretty.
Interesting aside – Pythagoras’s theorem works in not just 2 dimensions!