# The harmonic triangle

- Author:
- Luca Moroni

- Topic:
- Ellipse

## 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).
It is possible to drag the vertices of the triangle (A, B, C) and/or the starting point P0.
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.
The Ax and Ay parameters can be used to change the aspect of the springs.
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.
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.