Front end violently shaking

I was half way through a 4 hr trip when I hit a small bump and my 01 Tahoe starting violently shaking. I was going around 75 mph. I started too slow down and it stopped shaking when I reached 30-35 mph. I thought I had a blowout. I checked the tires and they looked fine. I continued with my trip(driving the same speed) and the problem did not re-occur. Two days later on my trip home I had the same problem.
I took it to my local mechanic and they said my tires were trashed and I need a allignment. I agree with him on both accounts, but I do not understand why bad tires would cause this type of problem.

Anyone expierence a similiar problem?