Switched reluctance motors (SRM) are characterized by rotor/stator pole pairs, in which the wound field coils in the stator poles induce magnetic reluctance in the rotor poles to create torque. However, noise development during motor operation is a key issue for this class of motors and much of the work to understand the acoustics and vibrations of these systems is limited to comparing experimental measurements with high-performance, multiphysics simulations. This work focuses on mathematical analysis of these systems through reduced-order modeling using both numerical and analytical methods, and the results are compared against experimental measurements of a typical SRM. To describe the underlying response of the experimental system, a circular shell model is developed for the stator, and electromagnetic finite element analysis is utilized to develop a physically motivated forcing profile for the experimental system. A numerical simulation model is then constructed by applying the calculated electromagnetic forces to the stator, and effective system parameters are determined by calibrating the numerical model to match experimental measurements. An analytical approximation is then derived by leveraging disparate timescales in the problem, and it is shown that the analytical solution accurately recovers the numerical and experimental results while also providing insight into the underlying physics of the experimental system.