Secondary propulsion methods for high-speed hyperloop transportation are sparsely researched. Secondary propulsion methods are essential to quickly, efficiently, and safely get a hyperloop pod up to its target speed from a stationary state. In this paper, we propose and analyze the feasibility of a form of electromagnetic secondary hyperloop propulsion, called a railgun, commonly used in modern-day artillery technology for high-speed ammunition launching. We assess the feasibility of two different materials and three different geometries for a railgun armature to propel a hyperloop pod. Inverse design of multiphysics simulation of multibody dynamics, magnetic fields, and electric currents are used for material selection of the armature that minimizes rail current energy requirements and the armature geometry that maximizes structural integrity.