Impact of k xⁿ Force on Potential Oscillations

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 xⁿ for even 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), Mathematica [1]-[3].