The resonance spectrum of small spheres of Mg with a spherical coating of MgO is calculated within the framework of the transition matrix approach. The spectrum for a concentric coating displays a single resonance peak, whereas when the coating is eccentric the spectrum becomes more complicated as the number of resonances increases. In the latter case, the spectrum undergoes evident qualitative changes according to the choice of polarization. Comparison of the spectra for dispersion of particles all having the same orientation with that for randomly oriented particles suggests a possible procedure to evaluate the fraction of particles that have a preferential orientation.