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The year, make and model info would help.
A pebble.
It's almost always a wheel bearing that would cause that noise.
Any number of things can cause a steering wheel to shake back and forth. It could be a bad wheel bearing indicating a wheel is about to fall off. It could be a bad tire or bushing. Without checking it out personally, I can't tell.
look back and when you turn your steering wheel left it goes right so turn the steering wheel the opposite way
look back and when you turn your steering wheel left it goes right so turn the steering wheel the opposite way
Either a bad wheel bearing or siezed brakes on that side or if it's rear wheel drive it could be a faulty differential.
I have to believe that it would be a bad wheel cylinder that controls the back brakes.
Repair or replace your reverse, neutral safety switch.
check the wheel bearing
Put it in reverse and don't turn the wheel. It's not rocket science.
Bad wheel bearing? Most likely a loose frt end component, Or the hub could be bent due to an impact.