You searched for: “tautochrone
That curve upon which a particle moving under the action of gravity (or any given force) will reach the lowest (or some fixed) point in the same time, from whatever point it starts.

A tautochrone or isochrone curve is the curve for which the time taken by a frictionless particle sliding down it under uniform gravity to its lowest point is independent of its starting point. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity.

This entry is located in the following units: chrono-, chron- (page 11) tauto-, taut- + (page 1)