The study presents results of first-principles modeling of spin dynamics in disordered ensembles of impurity-induced magnetic moments in a carbon spherical structure near 1% concentration of magnetic centers. Averaged signals of Rabi oscillations and their spectra are evaluated using a numerical algorithm based on direct calculation of quantum eigenstates. The Fourier spectrum includes a strong peak around the Rabi frequency and an additional rise in the low-frequency interval. Both peaks demonstrate the standard broadening proportional to the dipole interaction energy. Low-frequency oscillations are observed only for random spin clusters, while regular structures do not produce such dynamics. This effect results from quasi-periodic spin dynamics caused by random distances between particles and, correspondingly, the realization of a set of incommensurate eigenfrequencies in the spin dynamics. Thus, the low-frequency part of the spectrum can be used to characterize spatial disorder in ensembles of spin clusters.