A Reproducible Simulation‐Assisted Framework for Teaching Nonlinear Pendulum Dynamics in Engineering Education

ABSTRACT

Computer‐based simulation is increasingly important in engineering‐oriented STEM education, but students often experience mathematical modeling, numerical integration, visualization, and physical interpretation as separate learning activities. This study developed and pilot‐evaluated a reproducible simulation‐assisted framework for teaching nonlinear pendulum dynamics through one aligned workflow. Its distinctive contribution is the explicit connection of analytical model formulation, dimensionless state‐space representation, fixed‐step numerical integration, phase‐space visualization, Hamiltonian energy diagnostics, and assessment of students’ interpretation of the contrast between classical RK4 and symplectic Störmer–Verlet integration. The pilot implementation involved 30 undergraduate students who completed four computer‐assisted laboratory sessions over 12 academic hours. Learning outcomes were assessed using parallel pre‐test and post‐test instruments covering six dimensions: governing‐equation interpretation, phase‐space classification, energy‐based reasoning, numerical‐integration understanding, comparison of RK4 and symplectic integration, and visualization interpretation. The mean score increased from 48.2% in the pre‐test to 73.0% in the post‐test, corresponding to a mean paired gain of 24.8 percentage points. The paired effect size was large, with Cohen's d_z = 1.87, and the mean normalized learning gain was moderate, g  = 0.489. The strongest gains were observed in phase‐space classification and comparison of RK4 with Störmer–Verlet integration. These results provide pilot evidence that reproducible simulation, visualization, and energy‐aware numerical diagnostics can support short‐term computational understanding of nonlinear dynamics. Causal or comparative superiority is not claimed because the study used one cohort, no control group, N  = 30, one institution, and an immediate post‐test.