  Disordered viscoelastic materials are ubiquitous and exhibit fascinating
invariant scaling properties. In a companion article, we have presented
comprehensive new results for the critical behavior of the dynamic
susceptibility of disordered elastic systems near the onset of rigidity. Here
we provide additional details of the derivation of the singular scaling forms
of the longitudinal response near both jamming and rigidity percolation. We
then discuss global aspects associated with these forms, and make scaling
collapse plots for both undamped and overdamped dynamics in both the rigid and
floppy phases. We also derive critical exponents, invariant scaling
combinations and analytical formulas for universal scaling functions of several
quantities such as transverse and density responses, elastic moduli,
viscosities, and correlation functions. Finally, we discuss tentative
experimental protocols to measure these behaviors in colloidal suspensions.
