Possible cylinder misfire and/or failing engine mounts.
My 2000 V6 Sonata shakes while at idle also. I discovered I need an oxegen sensor and more importantly an "Idle Air Control Valve". 239.00 is the average and hard to find. .
Because the engine is running. Shut it off or give it gas and it will not idle.
below the throttle body... once you remove the intake hose, you will see it from the idle electrical plug
From my experience, If your crank sensors bad the car will not start up at all.
Hyundai accent idle speed
I have a 2000 sonata and I had the same problem. You may want to check the IAC and or clean the throttle body.
Let it idle when moving and get back to us.
Probably a misfire, it could be in need of a tune up.
You may have leak in the intake
it seems there a small screw back of the intake but the idle is control by the ecu.
may need tune-up
get a room stop phucking in it