A pendulum is suspended from the cusp of a cycloid cut in rigid support. The path described by the pendulum bob is cycloidal and is given by: x = a (φ − sin φ) y = a(cos φ − 1), where the length of the pendulum is l = 4a, and where φ is the angle of rotation of the circle generating the cycloid. Shat that the oscillations are exactly isosynchronous with frequency ω0 = p g/l, independent of the amplitude.