  The onset of rigidity in interacting liquids, as they undergo a transition to
a disordered solid, is associated with a dramatic rearrangement of the
low-frequency vibrational spectrum. In this letter, we derive scaling forms for
the singular dynamical response of disordered viscoelastic networks near both
jamming and rigidity percolation. Using effective-medium theory, we extract
critical exponents, invariant scaling combinations and analytical formulas for
universal scaling functions near these transitions. Our scaling forms describe
the behavior in space and time near the various onsets of rigidity, for rigid
and floppy phases and the crossover region, including diverging length and time
scales at the transitions. We expect that these behaviors can be measured in
systems ranging from colloidal suspensions to anomalous charge-density
fluctuations of "strange" metals.
