Abstract We propose a hierarchical modular framework to analyze a magnetic-mechanical oscillating system (MMO), integrating physical decomposition (leaf-spring mechanics, magnetic coupling, dissipation) with mathematical decoupling (normal mode separation, nonlinearity isolation).This dual-layered approach bridges component-level experiments with system-level dynamics, akin to domain decomposition in multiphysics simulations. By abstracting magnetic interactions as a nonlinear "pseudo-spring" and leveraging dimensionless parameter Ζ, we unify elastic and magnetic effects into a scalable pedagogical model. Experimental results align with COMSOL simulations very well (within 5% error when Ζ>20) , while theoretical extensions to Hamiltonian formalism demonstrate the framework’s adaptability to complex coupled systems.This work offers educators a reproducible platform to teach coupled oscillations, nonlinear dynamics, and multiphysics modeling, with open-source resources provided for classroom implementation.
Li et al. (Mon,) studied this question.