  This is the second in a series of papers on the effects of dust on
multifluid, MHD shock waves in weakly ionized molecular gas. We investigate the
influence of dust on the critical shock speed, v_crit, above which C shocks
cease to exist. Chernoff showed that v_crit cannot exceed the grain
magnetosound speed, v_gms, if dust grains are dynamically well coupled to the
magnetic field. We present numerical simulations of steady shocks where the
grains may be well- or poorly coupled to the field. We use a time-dependent,
multifluid MHD code that models the plasma as a system of interacting fluids:
neutral particles, ions, electrons, and various ``dust fluids'' comprised of
grains with different sizes and charges. Our simulations include grain inertia
and grain charge fluctuations but to highlight the essential physics we assume
adiabatic flow, single-size grains, and neglect the effects of chemistry. We
show that the existence of a phase speed v_phi does not necessarily mean that C
shocks will form for all shock speeds v_s less than v_phi. When the grains are
weakly coupled to the field, steady, adiabatic shocks resemble shocks with no
dust: the transition to J type flow occurs at v_crit = 2.76 v_nA, where v_nA is
the neutral Alfven speed, and steady shocks with v_s > 2.76 v_nA are J shocks
with magnetic precursors in the ion-electron fluid. When the grains are
strongly coupled to the field, v_crit = min(2.76 v_nA, v_gms). Shocks with
v_crit < v_s < v_gms have magnetic precursors in the ion-electron-dust fluid.
Shocks with v_s > v_gms have no magnetic precursor in any fluid. We present
time-dependent calculations to study the formation of steady multifluid shocks.
The dynamics differ qualitatively depending on whether or not the grains and
field are well coupled.
