A number of electromagnetic devices periodically driven by solid-state switches have been analyzed with time-stepping finite element method, which requires much time to reach a steady state. The sensitivity analysis which have been used for the shape design is employed for an efficient analysis of linear magnetodynamics with nonsinusoidal driving sources. The high-order frequency sensitivity from the time-harmonic finite element formulation is used along with Fourier transform and Taylor series expansion. The algorithm is validated through two numerical examples of a single-phase transformer and an induction heating system driven by a trapezoidal voltage source.