# Cycloidal Pendulum

Cycloidal Pendulum

This Demonstration illustrates the isochronous movement of the cycloidal (tautochrone) pendulum.

In 1656, Dutch mathematician and scientist Christiaan Huygens discovered that the simple pendulum is not isochronous, that is, its period depends on the amplitude of the swing.

He realized that the pendulum would be isochronous if the bob of a pendulum swung along a cycloidal arc rather than the circular arc of the classical pendulum. He proved that the cycloid is a tautochrone curve.

To construct this cycloidal pendulum, he used a bob attached to a flexible rod. The movement of the pendulum was restricted on both sides by plates forming a cycloidal arc. When the rod unwraps from these plates, the bob will follow a path that is the involute of the shape of the plates. Since the cycloid is its own evolute, this is a congruent cycloid.