Mystery vibration at 25 mph can't be diagnosed. It's not the front end!

Vibration story of my own. I had a my 65 on a side street driving home one night and I startred from a light. I felt a little shudder ans it passed. I then stopped at the next light and it came back again but stronger. NOW I'M LIKE WTF. So I take off a third time and the **** hits the fan at about 20mph. Ever see a grocery cart front wheel wobble? Thays what my entire front end was doing, it about rattled the mirrors off the car. I hit the brakes and it went away but I couldn't drive faster than about 15 or I'd get the shimmy back in a violent way. For it home and checked it out. Turns out the K member was cracked in 2 of 3 mounting points of the steering box. Another shimmy session and it would have let go completely. I found a 65 K about 200 miles away already pulled and painted so I made the trek and was home by noon, had it R&R'D in about 2 hours with the help of a cherry picker and some less than safe under the sling work. Problem solved. Good luck, let us know what the problem was after tou get the reason suspension torqued down.