%0 Journal Article
%T Impact of k x<sup>n</sup> Force on Potential Oscillations
%A Haiduke Sarafian
%J American Journal of Computational Mathematics
%P 58-65
%@ 2161-1211
%D 2025
%I Scientific Research Publishing
%R 10.4236/ajcm.2025.151003
%X It is common sense to assume, under the influence of modified Hooke law, that a spring-mass system should oscillate. A systematic numeric analysis proves otherwise. We have proven that the mentioned modified force subject to k x<sup>n</sup> for <i>even</i> n integers fails to produce oscillations. In contrast, the same format for odd n integers is conducive to harmonic oscillations. For the latter case, the impact of the chosen odd n values on the oscillation periods is mathematically identified. For selected cases, the corresponding oscillations are graphed. The analysis is based on applying a Computer Algebra System (CAS), <i>Mathematica</i> [1]-[3].
%K 1D Nonlinear Forces
%K Period Prediction
%K Harmonic Oscillations
%K <i>Mathematica</i>
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=141386