**Harmonic motion**

Finally, starting from the uniform circular motion, it is possible to define another type of movement, which is obtained by considering, at all times, the projection of the point *P* on the diameter *AB* of the circumference of the motion, i.e. the point *Q* of the motion (see fig. 4.4).

While *P* moves along the circumference, the point *Q* travels the entire diameter *AB* , moving back and forth, with a particular type of motion called harmonic motion. Now consider a series of arcs of circumference *AP*1, *P*1*P*2, *P*2*P*3, *P*3*P*4, *P*4*P*5, *P*5*B* , which represent the space traveled clockwise by *P* on the circumference from *A* to *B* , in successive instants of time *t* of equal length (for example, every second).

Since the circular motion is uniform, all the arcs considered must have equal length, which instead will not happen considering their projections on the diameter (see fig. 4.5) (this indicates that, unlike *P* , *Q* does not move uniform motion ). As can be seen from figure 4.5, while *P* moves from *A* (where it coincides with its projection) towards *P*3, the point *Q* travels segments of ever larger diameter until it reaches the center *O* of the circumference, coinciding with the projection of *P*3; after which the segments get shorter and shorter, until *P* reaches the opposite end of the diameter *B* , returning to be coincident with its projection. Ultimately, the motion of *Q* is accelerated from the extremes to the center, decelerated from the center to the extremes.

The hourly graph of harmonic motion is represented through a __sinusoid__ , characterized by an amplitude of the oscillation, coinciding with the radius of the circumference, which represents the maximum value of the elongation along the segment *AB* , and by a period that represents the distance between two consecutive ridges of the curve. Examples of harmonic motion are the motion of a __pendulum__ and a __spring__ .