Cycloidal Pendulum

Here's a video demonstration:
https://www.youtube.com/shorts/n2tWAdCFvtU

Further edits done in Tinkercad: https://www.tinkercad.com/things/9EKmdef4ihU-cycloidal-pendulum

The length of the pendulum should be set so that it extends to follow the lower curve from the hole at the cusp. This should allow the pendulum to swing with a period that is independent of the angle of the swing. The standard pendulum equation suggests that the period depends only on the length of the pendulum and the value of gravity. This is approximately correct for swings smaller than about 10º. The Cycloid Pendulum, first designed by Christiaan Huygens in the 1600's overcomes this problem by effectively shortening the pendulum length at larger angles. The careful analysis of the motion of a swinging pendulum was key in Huygens' invention of the pendulum clock.

The "Large 60degree" version is set to a smaller range of angles. This makes the support narrower. The maximum angle is achieved when the pendulu