Ford Falcon EL starts up and engine shakes like.

Hi mate, I had the exact same problem in the same exact car and it was actually an easy fix. After troubleshooting for awhile I decided it must be from the engine being too cold, which could be caused by having a stuck open thermostat (which in these cars is very easy to replace). So replace the thermostat - also a good time to do a thorough coolant flush - disconnect the battery for half an hour (to reset the ECU) and chuck in an injector clean than take your car for a drive and really get the revs up for awhile. It might take a couple of starts before your car starts perfect, it took mine about three days to relearn everything. If you're reasonably mechanical I would recommend replacing the spark plugs.

The reason an open thermostat causes this is because modern cars actually put in extra fuel after startup to heat the engine up quicker (a car runs more efficiently at a certain temperature) but with an open thermostat it is very hard for the car to get to operating temp so it continually puts in extra fuel, making the car drive like poorly. I reset the ECU to make sure everything it has learned while the thermostat is open will be forgotten. Also all that extra fuel probably left residue and carbon in the combustion chamber, which can stop spark plugs working correctly.

Before you do it I would just take a note of where the temperature sits before and after. Mine used to sit right on the bottom of normal but sits between the M and A now.