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Under load, while towing more than 2000Lbs, I'm getting a violent shudder when accelerating. It goes away when over 40mph, but till then it's bad. While not towing, there is no shudder, or at least it's not noticable.
Also, though not as important, my truck shakes on the freeway, over 60mph. The tires are fine, along with the bearings.
The truck only has 115K miles, but it was used on the farm for years. I just bought it for $800. It looks great, just has lots of little problems.
When was the last tuneup? Sounds ignition related to me. Low rpm under a load. Possibly torque converter shudder. When was the last fluid change? Maybe want to add Ford friction modifier when you do the next fluid change.
My truck was doing the same thing. I had the transmission fluid filtered & added an anti chatter agent. That helped a little. Then I found I had misfires on 2 or 3 cylinders. Replaced those plugs and wires & the problem disappeared.