  We study small oscillations of highly connected systems, which represent a
limit opposite to the more familiar case of disordered crystals. As a concrete
example we analyze the vibrational spectra of composite pendula. Remarkably,
these spectra exhibit universal behavior with non-vanishing zero-frequency
limit of the density of phonon states. This universality is captured by a
natural random matrix model for such systems. We analyze this model using
S-transforms of free probability theory and obtain the density of modes
explicitly, in the limit of large system size.
