this one is starting to get me, i have ruled out the tires for one. I only get this vibration/shaking at 60-65 mph and it very noticeable. had a tire shop check under the car and nothing was obvious?
Could be the rims if the tires are mounted in the same rims.
Does it do it at that speed in both 3rd and 4th gear?
Are you feeling it in the steering wheel or the seat?
Check your drive shaft u-joints. I had a similar problem years ago and the u-joint at the differential had at least 1/8 if not more of play. It had been bad long enough to take out my companion shaft too. I'd check it and if it's bad it's a cheap fix.
sometimes specific speeds match specific frequencies which cause a resonate type effect... for the speed at which it occurs... what gear are you in... does it occur at the same speed in a different gear, or does the speed change... if it is always the same speed regardless of gear, then it is from the driveshaft back... ford had a problem with bad driveshafts from the factory (just slightly out of balance or round, just enough to be ok until you got to this resonance frequency)... had a tsb on it (had mine replaced due to a similar problem, it would vibrate at a certain speed, then get better), also, on some cars, indexing the driveshaft makes a difference... has the driveshaft been out of the car recently... I would start with the driveshaft...