The second applet is a later version of the first. You can see that it starts with a much longer ladder--300 steps instead of 30, (which is more than just a ten times increase in difficulty). But this time a more powerful approach is used. (The square "target" is supposed to show scale. The ladder eventually curls up to fit into the center square.)

Your browser does not support Java, so nothing is displayed.

Connected springs can be described approximately with simultaneous linear equations. As long as the springs don't rotate much, the equations can be solved quickly. But because the ladder wants to curl, each solution to the equations causes a lot of springs to rotate, resulting in a new set of equations that needs to be solved, and so forth. This applet does manage to curl the ladder into a nice quiet hexagon in five or ten minutes. But I'm hoping for a still more powerful method.

Once again, you can start the applet over by scrolling to the top and hitting the browser's reload button.

The source for the first applet is FastMech.java; for the second applet, FastMech2.java.