The harmonic triangle

The harmonic triangle
Notes
To get a smooth dynamic it's better to download the applet and use it in the desktop version (Geogebra Classic 5).[br] [br]It is possible to drag the vertices of the triangle (A, B, C) and/or the starting point P0.[br]It's also possible to change the initial speed (v0x, v0y), the elastic constant k of the 3 identical spring and the damping coefficient μ.[br]The Ax and Ay parameters can be used to change the aspect of the springs.[br][br]The 3 elastic forces, summed together, result in a single elastic force attracting the free point P to the center of mass (centroid) G of the triangle. So, the total effect is that of a bi-dimensional harmonic oscillator, producing ellipses centered in G. [br]The springs are designed in Geogebra through prolate trochoids (cycloids) where the distance between consecutive coils is somehow proportional to the distance between P and the triangle vertex.

Information: The harmonic triangle