Probably insufficient idle speed. Most have a compensator to increase idle when it's turned on, use a tach to check.
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Most modern cars have an Idle Air Control (IAC) to control idle, and the computer handles it automatically. Some older cars, such as the 84 Caprice Classic, had an adjustable solenoid that stepped up idle when the compressor was on. If yours is one of these, make sure that the solenoid is extending when it should. In the case of the Caprice, it could be adjusted by turning the shaft via the nut on the end, but you should check your shop manual just to be sure.
Fast idle motor is not working. This is allowing the idle to fall below the threshold of what it should be when the A/C is on.
could be a broken engine mount.
loud, and shety muffler
The AC system will vibrate, and pressure throughout the system will be extremely high.
It is idling. This is hard for an engine to do smoothly.
Could be time for a tune up.
The most common cause is tire out of balance or bent wheel.
only when it is on, it causes slow acceleration
Adding heat causes gas molecules to vibrate, increasing the gas volume or pressure. A car with a damaged valve will usually vibrate noisily while operating. Tuning forks are designed to vibrate and thereby create a particular pitch.
If the tires are properly balanced plug tires should not cause a vibration.
Normally a bent wheel or tire out of balance.
it cause it to vibrate!