We continue the study of the properties of non-radial pulsations of strange dwarfs. These stars are essentially white dwarfs with a strange quark matter (SQM) core. We have previously shown that the spectrum of oscillations should be formed by several, well-detached clusters of modes inside which the modes are almost evenly spaced. Here, we study the relation between the characteristics of these clusters and the size of the SQM core. We do so assuming that, for a given cluster, the kinetic energy of the modes is constant. For a constant amplitude of the oscillation at the stellar surface, we find that the kinetic energy of the modes is very similar for the cases of models with LogQSQM = -2, -3 and -4, while it is somewhat lower for LogQSQM = -5 (here QSQM = MSQM/M; M SQM and M are the masses of the SQM core and the star, respectively). Remarkably, the shape (amplitude of the modes versus period of oscillation) of the clusters of periods is very similar. However, the number of modes inside each cluster is strongly (and non-monotonously) dependent upon the size of the SQM core. The characteristics of the spectrum of oscillations of strange dwarf stars are very different from the ones corresponding to normal white dwarfs and should be, in principle, observable. Consequently, the stars usually considered as white dwarfs may indeed provide an interesting and affordable way to detect SQM in an astrophysical environment.Facultad de Ciencias Astronómicas y Geofísicas