When I put my truck into drive... it kinda shifts hard. When I put it in reverse, you can feel it shift but its not as bad as putting it into drive. Maybe its because its an older truck? I keep my foot on the brake and shift into drive and you can feel it shift more than when you put it in reverse. I dont feel any vibrations under my seat when im driving... but I notice that there is vibrations coming from my passenger side door.. but maybe its because my truck is old and it can be anything? I also notice that there is a weird noise inside the cab like a vibration or something.. i cant really remember.. but I dont hear anything outside while the truck is running. The vibration inside the cab sounds like its coming from the drivers side somewhere inside the engine compartment or something. Although I dont hear it when the truck is running and the hood is open and im standing outside!

 

Usually you will hear a loud clunking noise switching from reverse to neutral and drive. Try to climb underneath the truck and try to shake the drive shaft on each end see if it wiggles at all. If it is bad be happy you have a chevy not at 04 F-150. Just replace the U joints on one the other day and it didnt have C clips instead for though it was better to press the bearings in :/ Let me know what u find

 

I had a similar issue with my 02' truck. It is a long bed and has the two piece drive shaft. It wasn't making the usual clunking when going into drive; but was vibrating from what felt like a corner of the truck. I assumed it was a bad belt in one of the tires. I ccouldn't find an issue with the tires or brakes. There didn't appear to be any issues with the drive shaft, even with the car jacked up letting the rear axle hang loose. I decided to remove the drive shaft (wasn't as hard as I thought it was going to be). It was one cup of one u-joint in the center section (front of rear shaft). I replaced it and the vibration and noise went away. I honestly never would have guessed that this particular symptom would have been the cause of a u-joint.