With the vehicle safely on stands, in neutral with park brake off...
...grab the drive shaft on each side of the U-joint with your hands and rotate opposite alternating directions. If you feel ANY slack the U-joint is bad.
Grab the shaft near the U-joint and push up and down, ANY movement in the U-joint and it is bad. Not to be confused with looseness at the spline at the transmission tail shaft, although if that is real loose it too can cause vibration.
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