Many things can cause steering shake. Wheels out of balance. ( including rear wheels ) Tryes out of round. Worn steering components. Worn suspension components. Even loose wheel nuts/bolts. Get it checked out for safetys sake.
Your power steering pump and or steering box may be about to give out on you.
Loose or worn steering parts, suspension worn, tires out of balance.
balance your tires
Worn steering or suspension parts. This can be very dangerous, so have this repaired ASAP.
There are several causes of this but the most common we call a head shake. This is when the tires shake side to side, the cure is to insure the steering is tight and you add one or two hydraulic steering dampers.
Wheels are out of balance
Tire out of balance, bent wheel, drive shaft bent, loose or worn steering parts.
Sounds like wheel balance, but check the steering dampner.
have front suspension checked
i would really like to know myself
Bad tire, bent rim, warped rotors.....
You may need a wheel alignment, or you may need bushings.