The following simulation try to illustrate the properties of cyclodial curves.
From conservation of energy: ,
However, from an intermediate point ,
So the amount of time is the same from any point.
1. A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line.
2. Cycloidal curves is the curve of fastest descent under gravity
3. the period of a ball rolling back and forth inside this curve does not depend on the ballís starting position.