Cycloid: Adjusting the Radius

Adjust the Equations

Recall, the equations for a cycloid from a circle with radius

are:

Suppose we make our circle larger. For example, let

. How do we need to adjust our equations?

The correct curve is shown in blue. Adjust the values for

, and

to fix the pink curve to match. Change the radius to

using the slider. Adjust

, and

again to make the curve match.

The equations for a cycloid created by a circle with radius rolling on the -axis are: ______ ______