Thanks for seeking advice on this very serious condition with your car. Front end shaking or vibration under acceleration is an indication of loose wheels, wear or even failure of the front suspension and/or steering components. You need to investigate this immediately and seek professional assistance if you do not feel that you have the ability to perform the following procedure safely yourself.
If you have the ability to check it safely (meaning have access to a level, paved surface, a jack and jackstands), raise the front end of the car and while someone is holding the steering wheel in a stationary position, place you hands on either side of the elevated tire and attempt to rock it back and forth, while keeping an eye on the tierods, steering rack and wheel bearings. Do this with hands at the 9:00 and 3:00 o'clock position on the tire/wheel, and then again at the 12:00 and 6:00 o'clock positions. The tire/wheel should be tight and under normal conditions, there would be very no or very minute amounts of movement. Any excessive movement would indicate worn compenents or components that are failing. Once you have determined the source of the shaking, you should proceed with fixing the car immediately.
〉 Answered on Oct 4th, 2012 by Karen Salvaggio, Owner - Professional Race Car Driver at Thunder Valley Racing