This activity belongs to the GeoGebra book The Domain of the Time.
By combining
two SHM with perpendicular directions, having the same period and in the same phase, we get a straight line. If we shift their phases, we get ellipses. If they also have different periods, we obtain
Lissajous curves.
As we will see later, the motion of a pendulum with a sufficiently small amplitude is almost identical to SHM. Therefore, the combined action of two perpendicular pendulums also produces Lissajous figures. These devices are called
harmonographs.