What is the cause of continual thumping (appears to be coming from back of car) and violently shaking?

Warped rotor, this would also cause the steering wheel to shake back and forth.

16 costly car noises - Bankrate.com

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BankrateYou should not ignore certain thumping, banging, clicking and squealing sounds. These sounds often rear their heads or intensify whenever the driver takes ... Hissing or sizzling under the hood: Heard when the engine is first shut off, .... my rear right wheel makes a loud bang when switching from park to drive/reverse.

Sounds coming from drivers side front wheel - AnandTech Forums

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Dec 1, 2009 - 21 posts - ‎10 authors
Sounds coming from drivers side front wheel The Garage. ... slightly left, I get a slight metalish-squealing sound coming from the drivers side front wheel area. ... but before I start the wild and expensive goose chase of bringing it to mechanics I ..... Those twoloud clunks when turning hard right give it away.

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CarGurusDec 22, 2009 - Thumping from front end - I have a hard thumping noise coming from ... without problem then I'll take a turn or something and it will start. ... I just recentlystarted having a rubbing and thumping and squeaking noise in the right front sidewhen driving ... Thumping sound coming from under the truck 4 answers.

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these cars are known for power steering pump issues I would start with the known issues on a car first to avoid wasted time and guessing outside of the known issues I would jump to possible brakes issues or other front end steering racks, axle or bearings but the last two are usually a knocking noise ,, brakes if they are shot will cause a loud grind, but so will bad power steering pumps. best of luck hope this helps..

the front brake disc is waving , out of end play ,,change front disc and you solve the problem
hope it helps

Here are the only reason that can cause a thumping noise

1. Wheel and Tire Problems
   • Wheels can become bent from striking objects, and tires can develop bulges from broken belts or wear. Both problems may cause a thumping noise. Thumping sounds caused by wheel and tire problems will typically increase in frequency at higher speeds, though the sound may not be heard at lower speeds. These problems can often be spotted by visual inspection.
   Suspension Problems
   • Worn or broken struts or strut mounts can create a thumping noise, especially when the vehicle hits a bump in the roadway. To test struts, bounce the rear of the car by forcefully pushing down on it and letting go. After letting go, the car should settle back to its original position without bouncing or noise.
   Loose Trim
   • Loose trim pieces near or in the wheel well can flutter in the wind while a car is being driven. These trim pieces may create a thumping noise as they strike other objects. A car owner can check trim pieces for looseness to determine if that is the source of the noise.

Hope this helps

sounds like timing chain or belt

The cause is too low an idle and engine is starving for fuel so it shakes like that.The thumping sound you hear is most likely just the exhaust being too close to the floor amd bumping against it when in drive with brake on.You said yourself that it stops when you put it in nuetral,well the engine speed goes up when there's no stress on it.With some one holding the brake and it's sitting there thumping,set the idle speed up just enough to make the engine stop rocking that way.

sounds like the flex plate on the back of the torque converter has splt across the bolt hols that hold it to the crankshaft

Okay, I had a problem like this with my 1990 Jetta, except there was no thumping noise. My steering wheel started to shake, that also make the whole front end wobble back and forth (side to side) - I took to a mechanic and had both whell bearing replaced. I must tell you that wheel bearing aren't something a mechanic can just check to see if they're good; once they get in there, it's a matter of just putting new ones in. Now, while different makes and models vary as far as cost of repair, (as well as mechanics prices) I paid a mere $400 dollars for my Jetta, which is a foreign made care, which also tend to cost more to fix than American made cars. Regardless, this is what it sounds like may be the problem with your vehicle. You may want to take it to a shop that specializes in alignments and brakes. It could be a loose brake caliper in the front. My brother had a car that was doing that same things, so we took the (front right) tire of, and he was missing both bolts that hold the brake caliper in place. Notice if the car brakes normally or not and if the shake increases, decreases or stays the same. If and when you take it to a mechanic, be sure to give them as much full detail as to what the car is doing so they can diagnose the issue as best as they can. This will save you from spending money on any unecessary parts and labor.

remove the belt and spin all of the pulleys by hand to make sure they all spin freely. the knocking noise is probebly a pulley locked up.