Rear end vibration

i have a 96 crown vic 4.6L v8 ,i just got it and all i did before i bought it was drive it around town , so i never got above 50mph ,well after i got the car i noticed that at about 45-55mph i get a real bad vibration in either the rear-end or the trans ,for just a sec. then it stops with no effect on the power or performance of the car ,what can it be ???

I would call the seller up and ask,just to see what is said. You have to do now what you should have done before purchase (was the car a gift) have it inspected.

Does this happen every time? Does it feel like rumble strips?

Take it Back!!! The seller knew about this and didn’t tell you. Just a guess, but it sounds like it could be a bad pilot bearing either at transmission output shaft, or if the car is so equipped, a bad carrier bearing supporting the drive shaft.

It sounds like the infamous 4r70w torque converter shudder, often remedied by a fluid flush and refill with Mercon V fluid.