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Quantum computing is becoming a major new field in engineering. Adaptation of classical computation concepts to this emerging technological reality is underway. In this study, a sampling-based approach is used to adapt state-domain equations to HHL-based formulation to obtain a homologous quantum algorithm for solving the dynamic equations in the state domain. The results obtained by the quantum computing approach are very close to the real response of the system and to the power-series-based exact solution. This work represents a significant contribution to the advancement of dynamic systems modeling and solving in state-domain adapted for use in quantum computers in the future.