Abstract:
By combining a pair of linear springs we devise a nonlinear vibrator. For a one dimensional scenario the nonlinear force
is composed of a polynomial of odd powers of position-dependent variable greater than or equal three. For a chosen
initial condition without compromising the generality of the problem we analyze the problem considering only the
leading cubic term. We solve the equation of motion analytically leading to The Jacobi Elliptic Function. To avoid the
complexity of the latter, we propose a practical, intuitive-based and easy to use alternative semi-analytic method producing
the same result. We demonstrate that our method is intuitive and practical vs. the plug-in Jacobi function. According
to the proposed procedure, higher order terms such as quintic and beyond easily may be included in the analysis.
We also extend the application of our method considering a system of a three-linear spring. Mathematica [1] is being
used throughout the investigation and proven to be an indispensable computational tool
