Dave is essentially correct, but I don't think that's where the problem is.
You'd have to have an absolute buttload of backlash in the ring & pinion for that to be causing a problem at that speed..
Same for the driveshaft. An improperly balanced shaft will cause a vibration, but it will be at higher speeds, and won't oscillate the rear suspension as you report.
I'm thinking you have an out of round rim, which is typical on duallie wheels, FORD duallie wheels in particular.
Think of Clint's issue.. he's trying to space out a wheel to keep it from hitting on his springs, and he's got to be careful he doesn't get too carried away with the backset or he's going to tear up wheel/axle bearings.
Same issue on a dual rear wheel. The center of force is not aligned with the center of load, and you can twist one pretty easily.