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 pendulum swings to be tangent to the last section of the curve. This allows a longer pendulum. The included rod will fit into the main design. When run through the hole and matched to the top surface, the bottom of the rod will be at a length for the placement of the center of a pendulum bob. The support is "bifilar" to keep the pendulum running nicely in a plane perpendicular to the support's curved surface.
Larger version can be found here: https://www.thingiverse.com/thing:6911797

See the Wikipedia entry for more information:
https://en.wikipedia.org/wiki/Cycloid#Cycloidal_pendulum