I am preparing a seminar on mathematical discovery for beginner's students, and one of the topics I plan to cover is the brachistocronic/tautochronic curve. For this purpose, I would like to let the students experiment with various curves connecting two given points P and Q for a while, trying to minimize the time it takes a ball starting at P to arrive at Q.
Since I cannot think of a feasible way to do it physically, I am looking for a suitable piece of simulation software. Ideally, one should be able to draw a curve and then have it simulate a ball rolling along that curve, showing the time it took at the end.
So far, I have been able to find this:
This is about what I want, but for my purposes, it is too "coarse" with just four adjustable points. Does anyone know of a piece of software that does this? Since it should be used by the students during class, it would be good if it was freely available online.