  When weakly jammed packings of soft, viscous, non-Brownian spheres are probed
mechanically, they respond with a complex admixture of elastic and viscous
effects. While many of these effects are understood for specific, approximate
models of the particles' interactions, there are a number of proposed force
laws in the literature, especially for viscous interactions. We numerically
measure the complex shear modulus $G^*$ of jammed packings for various viscous
force laws that damp relative velocities between pairs of contacting particles
or between a particle and the continuous fluid phase. We find a surprising
sensitive dependence of $G^*$ on the viscous force law: the system may or may
not display dynamic critical scaling, and the exponents describing how $G^*$
scales with frequency can change. We show that this sensitivity is closely
linked to manner in which viscous damping couples to floppy-like, non-affine
motion, which is prominent near jamming.
