I just woke up to hearing what sounded like a motor turning on and then turning off quickly. Its cool yet the a/c sounds loud & is starting and stopping... as soon as it sounds like its gotten itself going it stops and tries to restart again. Sometimes it will actually stay on for longer than 20 seconds. I do hear a louder vibration than what is normal.

If the noise is coming from the inside unit it is probably related to the inside blower.

Check to see if the wheel is tight on the motor shaft. Also check the motor mounts. All of this is located in the blower compartment.

Post back with findings.