The Hyperloop concept tackles the challenges conventional transport modes face, despite the considerable research gap. This research reduces the gap by focusing on the dynamic response of the periodically supported Hyperloop tube since the Hyperloop greatly exceeds the operational speed of traditional transport modes. Complexity is incorporated to obtain a detailed dynamic response using a finite element method. Progress has been made in incorporating the moving reference frame within the model with recommendations for the numerical stability of the transient analyses. Despite the computational inefficiency of the conventional non-moving reference frame, the model is utilised to conduct a parametric study. The study examines correlations between the stiffness properties of various Hyperloop elements, including the tube, rail, and the interface between the Hyperloop tube and column. These correlations are analyzed based on the system's response at the pod's location and the intersections between the tube segments. Here, the velocity of the pod is of paramount importance. Within the operational velocity range, only one critical velocity is identified, despite the system's infinite number of natural frequencies. The only dynamic amplification, identified as the main critical velocity, can be shifted beyond the operational range by increasing the overall structural stiffness. The shift can be realised due to the positive correlation with the main critical velocity and a negative correlation with the displacement difference at the interface between two tube segments relative to the structural stiffness. Within the research, the soil and pod interactions with the Hyperloop structure are excluded, leading to potential resonance with no risk of instability. The limitation can be addressed by modelling the pod as a mass-spring system and the soil as a two-dimensional medium. The files developed for the finite element models and the parametric study are available on GitHub (https://github.com/dedenner3/MasterThesis_Hyperloop). The files support reproducibility and further exploration of the methods described.