2005 Hyundai Accent rear end wheel or tire shimmy

Tires and Wheels problem
2005 Hyundai Accent 4 cyl Four Wheel Drive 24,101 miles

we just bought this car today, it has 24,101 miles. When you drive it 20 mph or less the car feels like the rear end is shimmying or shaking. When you drive it say 35 or faster it has no problem. I checked the tire pressure its okay. We checked to see if it was barrings be moving all of the tires, but they were fine. Can you tell me what the problem is. We are going to take it to Hyundai on Monday.
Thanks Linda