2008 Audi A6 - Vibrates

When I put the AC on, a vibration effect is felt as if something is loosened in the engine but the AC cooling effect is fine. Any idea what the issue might be?

The extra load the AC places on the engine may cause a rough idle. You might be overdue for routine maintenance such as spark plugs, air filter etc.
you could also try a can of fuel system gasoline additive such as SeaFoam.

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