This is typically caused by severe wheel alignment problems. Bad suspension components (e.g. shock absorbers) can cause this also.
Tune up
Engine miss at idle. Can be caused by vacuum leak.
http://www.2carpros.com/topics/shakes1.htm
It could be a shifted belt in one of the tires.
bent wheels or a broken cord in a tire or a deformity in a tire.
Perhaps front rotors are "out of round" and need to be either re-surfaced or replaced
Perhaps spark plug wire got disconnected in error?
If it varies with driving speed, look for an out-of-round tire. If it vibrates only when braking, you probably have a warped brake rotor.
It's PROBABLY a wheel balance problem. It just happens that that's the resonance frequency of the suspension.
Sounds like an engine misfire. Can be bad spark plug, plug wire, fuel injector, or bad coil on plug.
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It may hesitate, start poorly, or idle rough. You may also have problems when you give the car a lot of throttle while driving as the car will not get enough fuel to accelerate. The car may shake and sputter. You are better off changing the filter every 30K miles and avoiding having to worry about it.