vibration unknown
Sounds like something is moving and binding in that position when you stop hard, the pop is when it returns to where it should be.
Something I have seen before is the spring center bolt shears off, which lets the axle shift to the front or rear.
You should be able to see an indication of that happening by looking at the U bolts that bolt the axle to the spring or by measuring the distance from the axle to the end of the spring on both sides and comparing measurements.
If that is happening in either axle, the driveshaft slip joint could be to close or to far open and causing the vibration.
On mine, the front axle to frame clearance was getting close to nothing, I thought the springs were getting weak.
When I hit potholes, I had this strange clunk I could never find.
So when I was changing the front springs, when I dropped the front shackles down out of the frame, I found why it was ridding low and where the clunk was originating from.
The upper bushing in the spring shackle was gone, the holes in the shackle side plates had worn to almost twice the size they should have been and the bolts were worn down to about 50% of what they should have been.
Just for grins I changed both of the front shackles and left the original springs under the truck to see how much difference they made, then I change the springs.
The difference in ride height was all in the shackles, the original springs were just fine.
That did not cause a vibration, but it the bolts/bushings on the rigid mount, rear front axle or front rear axle were worn, that would let the axle be out of line as well.
About 250,000 miles is when I went through all that with mine.



