I don't think any pulley shaking whilst rotating is ever considered normal , Correct me if I'm wrong but by the way you described it, it sounds like the Crank Pulley? if so then im pretty sure its not supposed to shake and wobble lol? I think you should get that checked asap. Not really sure how much it would cost depending on how bad the outcome maybe. Have you tried to physically exam it? if there are any screws missing or any irregularity? does the engine seem to idle fine?
Will sub to this thread, may come in handy if it happens to me >.<!