Lateral Oscillations in rear of 2000 Nissan Frontier.

[nissanup]

I have a 2000 Nissan frontier. When I push laterally with my hands on the rear end of the truck, and let go, the truck oscillates laterally (left/right) about 6 cycles. Is that abnormal? My old 1988 hardbody datsun does not do this. When I do the standard up/down test, it doesn't oscillate at all. That is,
if I push down on the rear of the truck and let go, there are no oscillations. I am running the rear tires at 20psi instead of the recommended 26psi, but that is because of issues with my neck/back, in which I needed to soften the ride some, as the rear tires are the all-terrain ones with very hard rubber.