71 mustang shake at 45mph

if i drive the car to 45mph or 50 i can feel the car shake almost like a wheel is out of balance. as i go faster so does it. if i accelerate it goes away. but at cruising speed or slowing down i can feel it. any ideas? i checked the drive shaft for play but it seems ok.

Have you recently removed the drive shaft could it be 180 degrees off @ the u joint mount?

1) Speed balance wheels.
2) Check engine & transmission mounts.

I restored a 71 Mustang convertible a few years ago. Early Mustangs shock towers had a propensity to bend inward towards the motor' That causes camber/caster and tow in problems. A fender brace solved a lot of those problems. Also the design of the coil over spring suspension created a bump steer problem with those cars. Heavier stabilizer bars and shocks helped.
http://www.vintage-mustang.com/ That site has all the information you will ever need about your car.