Tautochrone (Cylcoid) Pendulum

In 1673 Huygens realized that forcing a point mass to fall along a cycloid would make the time to the bottom the same no matter where you started. He also knew that he could arrange for that to happen by making that point mass be that of a simple pendulum as long as the pendulum rope wound on a pair of cycloids as it swung. Originally it was hoped that such an approach would lead to more stable timekeeping, a.k.a. the longitude problem.

Here is a print of such a set of cycloidic 'cheeks' for the pendulum, shown with Johnny G. setting up and doing the measurement (data shown) using a basic lab timer in most physics classrooms. It seems to work quite well!

extra for experts is enclosed a brief derivation of this tautochronic behavior using lagrangian mechanics.