Your air conditioner shouldn't shake, rattle, or roll when it's running. In fact, with a properly working unit, you shouldn't be able to pick up any vibrations from the unit unless you are actually touching it. If you are noticing movement when the AC is on, it's time to do some troubleshooting. The following guide can help.
Issue #1: Unsecured housing
The housing is the exterior of the unit. The housing may be a single piece that slips over the unit or may consist of several panels that are screwed into place. Begin your inspection by making sure all the panels or the housing unit as a whole is fully secured to the AC system or the pad beneath. If any part of the housing is loose, it may rattle and shake when the blower fan is running.
Issue #2: Loose blower
Sometimes the screw that holds the blower fan works loose. To check for this, begin by cutting the power to your unit. Then remove the housing so you can see the motor and fan. Using a screwdriver, make sure the fan blade is firmly affixed and not wobbly.
Issue #3: Damaged fan
Sometimes the issue is the blower fan, yet the fan isn't loose. Try spinning the fan manually. If it wobbles, but the screw is tight, then there is likely a balance issue. This could be caused by a warped fan blade or minor damage to one of the blades. The best option is to replace the blade with a new fan blade.
Issue #4: Dirty interior
Sticks and other debris sometimes get into the housing, where they are then banged around by the blower each time the AC is running. This is a simple problem to recognize and repair. If you see debris when you remove the housing, either scoop it out or vacuum it out with a shop vacuum.
Issue #5: Missing padding
Some larger units will simply vibrate more than others. Fortunately, there is a way to fix the problem. You will need to install an anti-vibration pad beneath the AC unit. These pads consist of a wooden core sandwiched between rubber dampeners that absorb any vibration. Fencing in the unit can also help prevent the noise vibrations from traveling far. Just make sure the fence is placed far enough away from the AC unit that the fencing doesn't interfere with air flow.
For more help with your AC, contact an air-conditioner repair technician in your area by visiting sites such as http://www.capefearair.com.