The increasing need for a fast, efficient, and environmentally sustainable transportation paradigm has pushed growing interest towards the class of magnetic levitation trains. In this scenario, the Hyperloop concept has been subject to special attention,given its capability of reaching ultra-high speeds (up to 1200km/h). However, the feasibility of this technology is entangled to the stability of its electrodynamic levitation system. State of the art literature provides a method for accurate modelling of the coupling between the electrical and mechanical domains in the Linear Time Invariant systems framework: this technique allows to easily identify the unstable behaviour of the device and remove it by introducing additional damping through a secondary suspension.