Chrysler Repair: Vibration in the speed range of 35-50 mph, tie rod ends, radial runout

Question
My convertable Chrysler Le Baron starts violently shaking after I accelerate over 30-40 miles after the 46 mile mark it stops, and if Im on the freeway when I have to decelerate it begins to shake when i hit around 60 ... I've checked the tires alignment was check not to long ago, what are the possible scenarios that can be afflicting my car?  

Answer
Hi Jorel,
Shaking that occurs in the middle speed range has been associated with the tire/wheel combination not being perfectly round. It has to be round to within about 0.04" as measured at the middle of the tread. To correct the tire mounting shop will remount the tire to the wheel to try to cancel out the out or roundness in what is called a match mounting procedure which takes advantage of the tire and wheel individual out of roundnesses and cancel them out. So check the radial runout and see if it differs by more than about 1/16" by jacking up the wheel and spinning it and measuring the variation. That is one good possibility. Tie rod ends could be loose would be another possibility.
Roland