Modeling, Simulation, and Analysis of Mechanical Systems in Universal Vibration Damper Apparatus Using MATLAB Software

Abstract

This study presents modeling, simulation, and analysis of a mass–spring–damper (MSD) system for characterizing the physical parameters of mass (m), damping (c), and stiffness (k) using standard MATLAB without the need for additional toolboxes. Experimental data is realistically synthesized through combined step + multi-level sinusoidal excitation to enrich frequency information, then small Gaussian noise is added to the displacement measurement to mimic sensor limitations. Parameter estimation was performed in the time domain by minimizing the squared difference between the model response (the result of ODE45 integration) and the measurement data using fminsearch (Nelder–Mead). Model performance was evaluated through out-of-sample validation on different inputs (chirp + small step) and Monte Carlo sensitivity analysis (±10% around the estimated parameters) to assess robustness to parameter variation. The results show high model fit on the training data and remain robust on the validation data, with residuals showing no systematic patterns and consistency of natural frequencies and damping ratio ? with synthetic reference values. The practical contribution of this study is a concise but comprehensive click-run workflow, including data generation, estimation, validation, and visualization, which can be used as a template for damper testing in laboratories, final projects, and initial diagnosis activities in low-order linear mechanical systems.