There are a number of possibilities:
Your automobile may have a tire out of balance or a worn part in the front end causing this "shimmy" effect .
because it shakes the world and knocks everything over.
Steering wheel shakes
Warped rotors
allignment
could be bad alignment
usually steering shakes over 60 mph is due to front tires needing to be balanced unless you have something more serious going on.
I have seen this with bad or unbalanced tires.
Tires out of balance, bent wheel, tire defect, or suspension or steering parts worn.
it shakes to the right or left
You probably have rusty/scored brake rotors.
Wheels are likely out of balance