Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire (Advances in Applied Mathematics and Mechanics, 2021)
The exact analytical expression of the period of a conservative nonlinearoscillator with a non-polynomial potential, is obtained. Such an oscillatorysystem corresponds to the transverse vibration of a particle attached to the center of astretched elastic wire. The result is given in terms of elliptic functions and validates theapproximate formulae derived from various approximation procedures as theharmonic balance method and the rational harmonic balance method usuallyimplemented for solving such a nonlinear problem.