Air conditioner only makes low pitched whining noise when squirrel cage is coming to a stop after turning off the motor.

Mount problems you can usuallytell by moving the motor manually.

It could also be a bearing problem. You'll, again, typically notic some amount of friction in the motor when spinning it by hand.

The cage itself will not make a noise as long as it is tight on the motor shaft. It could be the motor bearings (usually sleeves not actual ball bearings) could stand to be lubricated but in many cases the motors are lubed for life without a place to actually oil them.

Kill the power and reach into the cage area and see if you can move the shaft in or out or up and down. Too much slack usually indicates the motor is well worn and could need to be replaced. Remember to get a new motor capacitor that matches the new motor you buy.