Wei, DongmingLiu, Yu2016-11-232016-11-232012Dongming Wei and Yu Liu; 2012; Some Generalized Trigonometric Sine Functions and Their Applications; Applied Mathematical Sciences; http://nur.nu.edu.kz/handle/123456789/1915http://nur.nu.edu.kz/handle/123456789/1915In this paper, it is shown that D. Shelupsky's generalized sine func- tion, and various general sine functions developed by P. Drabek, R. Manasevich and M. Otani, P. Lindqvist, including the generalized Ja- cobi elliptic sine function of S. Takeuchi can be defned by systems of first order nonlinear ordinary differential equations with initial condi- tions. The structure of the system of differential equations is shown to be related to the Hamilton System in Lagrangian Mechanics. Numer- ical solutions of the ODE systems are solved to demonstrate the sine functions graphically. It is also demonstrated that the some of the gen- eralized sine functions can be used to obtain analytic solutions to the equation of a nonlinear spring-mass system.enAttribution-NonCommercial-ShareAlike 3.0 United Statesgeneralized sineHamilton systemnonlinear springvibrationanalytic solutionArticle