My '88 F450 bucket truck did the exact same thing when I bought it. I hit a little washboard on an on ramp one day and thought I was going over the embankment at 45 MPH.
I took it to the best front end shop in town and said FIX IT! Everything under the truck was tight, including the panhard bar and bushings. He had a roller on an electric motor that he spun the front tires with. The left front started ocillating at speed and he said, you need new a new tire, although it looked good. He also said if the steering started feeling funny on this truck to check the bushings in the panhard bar and put a steering stabilizer on it.
Since the installation of the new tires, I've gone over 12k miles death shake free.