You don't give us the model number of this mower, therefore we don't know if it is a 2-cycle or 4-cycle model, as they offered both types during this period. The first thing that comes to mind is a bent crankshaft, which is much more common on the 4-cycle models, and in essence, you probably should just replace the mower if that is the case. A badly bent blade could also cause this problem. Also the motor coming loose from the deck (or muffler plate on 2-cycle models). But I would have to say that a vibration as large as you describe generally comes from a bent crankshaft, caused by hitting a very big unyeilding rock. Now, on the 2-cycle models, I have seen this crack the crankcase rather than bend the crankshaft.
