50-60 mph issues sometimes are a result of a tire issue. At those rotational speeds, broken belts, out of balance and other tire issues tend to be very noticeable if everything else is good.
Infamous "death wobble" occurs around those speeds as well. Shaking appearing at a certain speed and then disappearing at a faster speed or during cornering/braking. Worn or loose front components (suspension/steering) that have slop in them cause "death wobble" .... mostly front wheel bearings, tie rod ends, CA bushings, Idler arm/mount, etc. With slop in them, they can vibrate/oscillate at a certain speed and then as forces increase on them (steering angle, braking, suspension load/unload), those forces tend to dampen the oscillation/vibration. Imagine a loose front wheel wobbling. Then toe (adjust) the front wheels in or out a bunch and the force pushes the loose wheel to its limits in or out and stops the wobbling. We Jeeper's deal with this on a very regular occurance (Google Jeep TJ Death Wobble). That's my bet.
Also, it could be missing transmission mount bolts.... As was my issue.
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