Dynamical properties of Nonlinear oscillators by the variational iteration method

This research paper details an innovative way of investigating nonlinear oscillatory systems by combining Laplace with the Variational Iteration Method (VIM). The specific focus is on basic pendulum, mass-spring oscillators that embody the duffing equation. Finding the Lagrange multiplier, which is important for LVIM [32], is highlighted as a crucial step in resolving nonlinear issues. The paper argues that the Laplace transform makes the Lagrange multiplier easier to find, which makes the LVIM more accessible to academics working with nonlinear situations. The main goal of the research is to provide a comprehensive analysis of the dynamical features inherent to nonlinear oscillators, particularly resonance, bifurcation and chaotic events. By utilising LVIM, a rigorous analytical approach, the research aims to enhance the basic comprehension of nonlinear dynamics. The authors argue that by combining the two approaches, theoretical insights are improved and VIM with Laplace becomes a powerful and accurate instrument for mathematical modelling with possible uses in physics and engineering.