Wheel balance, Worn steering parts, Worn suspension parts, Tire damage,
Check or replace axles, worn axles are primary source of shaking when accelerating.
check the motor mounts
Loose Motor Mounts
Sounds like either you have a bent rim(s) or your tie rods are going.
you probably have a bad ball joint.
My Dodge Charger doesn't shake...
A 2002 Dodge Caravan may shake back and forth while driving due to several potential issues. Common causes include unbalanced or damaged tires, worn-out suspension components, or misaligned wheels. Additionally, problems with the drive shaft or issues with the brakes, such as warped rotors, can also lead to vibrations. It's important to have the vehicle inspected by a qualified mechanic to identify and address the specific cause.
Probably the throttle position sensor.
it will shake uncontrolabley
I would first look for a vacuum leak.
where is the shaking coming from? where do you feel the shaking , is it the entire car , steering wheel?Answershaking can also be caused by worn out engine mounts. Well, I have the problem (have had it for years now) and so far four mechanics have tried everything including new engine mounts, new front bearings (they were noisy anyway), new axle shafts, and so on but no-one can fix the problem. Still looking for an answer - GlennAnswerShaking occurs when a portion of the vehicle has a mechanical resonance frequency which receives energy from another connected source. This could be a multiple of the shake frequency, not just the identical wave frequency. e.g. The front end resonant frequency might be a multiple of the Tire rotation frequency or the engine / drive frequency. The only solution is to change the shaking section (Usually the front-end suspension) frequency. This may involve significant modifications.You might want to check the drive shaft if it is all wheel drive. I have the same problems with a 2000 Grand Caravan 3.8. Havent found the parts yet.