An Investigation of Spatial Energy Distribution in a Harmonic Oscillator and the Golden Section

Since harmonic oscillations are defined as "periodic time dependent changes of physical quantities," the high school physics curriculum focuses on the time dependent physical quantities of the harmonic oscillator, such as velocity, acceleration, and energies. The spatial dependency of physical quantities, particularly the spatial distribution of the three energies in a harmonic oscillator system, which continuously vary their amount.: kinetic energy (Ekin ), potential energy (Epot ) and elastic potential energy (Eepe ), is the focus of our concern in this study.. Some 11th grade students from the German high school in Istanbul (zel stanbul Alman Lisesi) came up with the idea on1May 2015.

The golden section, we discovered, has a significant impact in the spatial energy distribution, particularly between potential and elastic potential energy. We looked into its involvement in the harmonic oscillator in this research. The role of the golden section has only been acknowledged in more intricate systems, not in such a simple system as the harmonic oscillator. We discovered parallels between our findings and the role of the golden section in the KAM-theorem and Burgers-turbulence. Indeed in our investigation the system is stable and we cannot choose between two frequencies, but the golden section is integrated in the energy relations.