Therefore I still have trouble to embed “my” equations in my text (view the German essay), here you will find only a short description of the happenings on the German page:
A short introduction leads to the term “sine”, a spring stands for an oscillation.
Equation 1 (Hook) and equation 2 (Newton) will lead us after some differential math to equation 7 with the solution (8) and, more clear, to equation (10).
The last equation shows the mighty point of view of Fourier/Helmholtz:

Every periodical event (not only oscillations!) can be interpreted as a sum of harmonical oscillations.