Engine RPM will raise after engine is warm. This

which engine.??? never post lacking engine ,here is why.
1.3 L G13B I4
1.5 L G15A I4
1.6 L G16B I4
1.8 L J18A I4
1.8 L BP-ZE I4
1.9 L XUD9 diesel I4

Ill answer in the generic and for GAS engines. only.
that is illegal RPM, the ECU regulates it to 800 all the time
that means the ECU can not regulate the RPM now, for many reasons.
and sure it vibrates too low, that is normal for all 4cylinders to do that.
no bad engine mounts never lower RPM to 600, ever.
they dont control idle speed at all.
the #1 reason for most cars to idle too low are:
1: EGR leaks, (clean it)
2: ISC stuck closed (electric idle speed acututor dirty) clean it.
3: gross misfiring , caused by bad spark or bad fuel mix.
4: low compression on 1 or more cylinders (real low) Do compression test at WOT. throttle.

Well, the computer is supposed to open the IAC to keep the RPM above 600 or so depending on the load on the engine.
If you have voltage and ground for the IAC it should raise idle speed to at least 1100 when you first start the engine cold.
If that is not happening, I would look for carbon build up in the throttle body. You can apply voltage to the IAC and open it to see if the air passage is open too.

Hi, what happens is the rubber part of the motor mount splits or comes unglued from the metal and allows the engine to lift up when the engine is torqued. Look carefully at each motor mount while an assistant holds the brake and shifts the car between reverse and forward. One ot both of the mounts will separate when they give the car a little gas (in gear but holding brakes down so as not to move). Replace the broken motor mount by carefully lifting the engine slightly using a floor jack with a block of wood. The mounts are held on to the frame by bolts and are attached to the engine by long thru bolts. Please let me know if you have more questions, and thanks for using FixYa.

600 - 750 RPM

its the tps

egr could verywell be the problem leaks after warmup

could be numerous reasons. this is your best bet take it in to a mechanic and have your engine codes scanned. it is a minimal charge, some even do it for nothing it only takes 10 minutes.this will point you in the right direction.

it will do that, it is normal, should go between about 600 and 1500 rpm...
----------- thats just a normal warm up cycle, it will change the engine speed and mixture as combustion gets better with the heat.

if it only does this when its cold its normal, the car is just setting a higher idle to warm up the engine

Check your EGR or your Idle control Valve. This can cause a problem with your irratic idling