Periodicity: a wheel rolling without sliding

Author:
a.zampa
This applet simulates a wheel rolling without sliding. The point in the abscissa axis corresponds both to the time and the angle of rotation (the angular velocity is 1 rad/s), the initial position is that shown on the left. The graph represent the function relating the height (relative to the ground) of the red point and time.
Try moving points and and observe how the graph changes. Then enter the function representing the heigth of at a given time ( for GeoGebra) and verify that corresponds to the plotted graph (remember that when the initial angle is and that the maximum height is the diameter of the wheel).