Tire out of balance or bent wheel.
low fluid would cause this or the pump could be going out
you have a bad cv drive shaft
Lowering the springs of a car will cause the tires to bounce.
Wheel balance, bent rim, bad tire or worn steering components to name a few.
check motor and transmission mounts first. check steering and suspension parts.
About the only thing that will cause the wheel to bounce on any car is the strut being bad.
gum
Low steering fluid can cause a steering wheel to whine when turning. A worn steering belt can also cause a steering wheel to whine when a car is being turned.
You may want to check this with your dealer, but not too recently the cav and sunfire had a recall on the power steering. Something about a bad gear and power failure when making left hand turns. They would either replace the faulty gear or the whole rack and pinion assembly. Either way have it checked out. A steering problem is not a nice problem. It may cause accidents or death.
If the sound occurs only when turning, (left or right) the most likely cause is a loose power steering belt. First check to see if the belt is tensioned correctly, or in need of replacement.
Low power steering fluid or defective power steering pump.
with me it was the o2 censer