When in gear and stopped, it will idle low and sputter but when put in nuetral this goes away. What's the problem?

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.

when you want an answer, you must include details like make , model year , efi, type of equipment because what you have provided is not going to get a viable response
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o-2 sensor

Could be a plugged up fuel filter or air filter, water in fuel, now common with E85, E10 ethanol...

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it sounds like a vacuum leak to me, my car had the same problem but when i changed the hose that connected the valve cover to the fuel injectors the rpms dropped back down to about 800 rpms

Way more info is needed. Check the fuel filter. Could be plugged just enough to starve at a low idle but gets enough when you have higher rpms. Does it sputter at an idle? Could be so many things, to electrical, including needing the carburetor rebuilt.

your idle speed too low.take it to a dealer.they have to reset idle.it should be 600-800 rpms.when you turn on air conditioner.the computer steps up idling to keep engine from stalling .your curb idle too low.

there was a tsb on those for the neutral switch. it can cause all sorts of funky problems. usually you get a check eng. light with egr code and imrc code. can cause erattic idle, stalling, and alot of confusion. it is located behind a bracket under the transmission. you can check continuity wile putting the shifter in and out of gear. also there in a tsb on the clutch pedal switch that can do the same thing. you can look under the dash and make sure that the rubber stopper is completely engaging an diengaging the switch, and you can check continuity there as well. hope this helps you... dustang

motor mount or tranny mount.

Try this
Here are the most common causes of surges, stalls at stops, low erratic idle speed, rough idle and engine hesitation, it is in most cases the idle speed control air-bypass valve and or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.