With your limited info there could be many reasons but first have you tested the cold cranking amps on the battery? The charging system may be fine but if the battery is going it could cause the problem your describing.
Turning on the radio will not cause your car to vibrate. The only thing I can think of that would even be remotely possible is that the alternator is barely working enough to keep the battery charged. The extra load of the radio could possible cause the engine to miss. This is highly unlikely, but remotely possible. Have the charging system checked.
Over or under charging.Another answer:Typically that means that the computer has detected a problem with the alternator. In more sophisticated systems, it can mean that the computer has detected a faulty diode and even thought the alternator is still barely functioning, you'll probably want to take care of it soon.
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