Interactive Simulation with GeoGebra for Damped Systems with Base Excitation
DOI:
https://doi.org/10.23925/2237-9657.2024.v14i2p009-030Keywords:
vibration, resonance, interactive simulationAbstract
This work addresses the modeling, analysis, and simulation of a damped system with base excitation, using the Lagrangian formalism to derive the equations of motion. The simulation was developed in GeoGebra and allowed for the visualization of the system's behavior. The results indicate that when the damping factor ξ is less than 1, resonance occurs as the excitation frequency approaches the natural frequency of the system, resulting in significant amplifications of the vibrational response. For ξ ≥ 1, the resonant behavior is eliminated, highlighting the role of damping in dissipating energy and controlling the dynamic response of the system. In addition to the quantitative analysis, the interactive approach proved to be an effective tool for understanding phenomena such as resonance and displacement transmissibility. The simulation allowed for the visualization of the transition between the transient and steady-state regimes, highlighting the influence of damping on the dissipation of initial conditions.
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