I've had the random vibration just like that on my 02 F350 on a couple of different occasions.
First time it was bad wheel bearing hub...literally felt like I was driving on the rumble strips and would usually happen after driving over a something like a bridge transition. It would last a couple of miles and then go away. I pulled the hub and the bearing rollers just all fell out.
Second time it happened it was the exact same feeling but would just happen at random times. Ended up being rear brake cable had come unhooked. That was a hard one to track down because it felt just like it was coming from left front end, but was caused by rear left brake. Had to take it to mechanic to find the trouble and he said it fooled him too.