variational approach for approximate analytical solution to non-natural vibration equations

in this study, he’s variational approach (va) is used to solve the non-naturalvibrations and oscillations. the method works very well for the whole range of initial amplitudesand does not demand small perturbation. it is also sufficiently accurate to both linear and nonlinearphysics and engineering problems. we consider some examples to illustrate the effectiveness andconvenience of the method. runge-kutta’s [rk] algorithm was also implemented to show theexamples through a numerical method. finally, to show the accuracy of the va, the results havebeen shown graphically and compared with numerical and exact solution.