In many small-scale devices, the materials employed are functionalized (doped) with microscale and/or nanoscale particles, in order to deliver desired overall dielectric properties. In this work, we develop a reduced-order lumped-mass model to characterize the dynamic response of a material possessing a microstructure that is comprised of an electromagnetically-neutral binder with embedded electromagnetically-sensitive (charged) particles. In certain industrial applications, such materials may encounter external electrical loading that can be highly oscillatory. Therefore, it is possible for the forcing frequencies to activate the inherent resonant frequencies of these micro- and nanostructures. In order to extract qualitative information, this paper first analytically investigates the mechanical and electromagnetic (cyclotronic) contributions to the dynamic response for a single particle, and then quantitatively investigates the response of a model problem consisting of a coupled multiparticle periodic array, via numerical simulation, using an implicit temporally-adaptive trapezoidal time-stepping scheme. For the model problem, numerical studies are conducted to observe the cyclotronically-dominated resonant frequency and associated beat phenomena, which arises due to the presence of mechanical and electromagnetic harmonics in the material system.