A bead is sliding along a rail
without friction under the action of gravity. The bead starts with
zero initial velocity from a point taken as the origin of our
Cartesian frame of reference to a point (L,H), with the y axis
pointing downward in the direction of gravity.
Calculate the travel time of the bead in the case of a straight
rail as well as when the rail as the form of a cycloid
x=R( a - sin a), y=R (1-cos a).
Compare both times as a function of L and H .
Display your data in a way that is easy to communicate.