This research work introduces a novel dynamic model to predict the vibrations of ballasted railway tracks under dynamic loads generated by wheel-rail interactions. By integrating Euler-Bernoulli beam theory with Floquet's theorem, the model effectively captures the periodic nature of the track structure and incorporates the viscoelastic properties of the underlying foundation. Rigorous numerical simulations demonstrate the model's accuracy in predicting rail deflections, validating its reliability and precision. The study emphasizes the crucial role of rail-support interactions in influencing track dynamics, particularly resonance phenomena. The findings offer valuable insights into the behavior of railway tracks under asymmetric loading conditions and complex support configurations, enhancing our understanding of track performance. The analytical calculations of rail displacements, corroborated by MATLAB simulations, further demonstrate the model's applicability and robustness.