# Ball rolling down curve simulator

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:

https://www.physicsclassroom.com/Physics-Interactives/Circular-and-Satellite-Motion/Roller-Coaster-Model/Roller-Coaster-Model-Interactive

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.

• Good question! One thing that came to mind is desmos and their marbleslides. (Example link: teacher.desmos.com/activitybuilder/custom/… ) I have used these in activities where students have to adjust the function so the marbles roll down the curve and "collect the stars." I am not sure if it's possible to modify this to exactly your needs, but I can at least guarantee this kind of thing allows students to modify the function formula and then click a button to set the marble in motion. Feb 23, 2022 at 19:54
• I was also thinking of desmos. Can you write the functions as functions of time, to include the physics? Feb 23, 2022 at 22:35