98 Ram Vibration Noise

I have a 98 Dodge Ram with the 5.9L. At speeds around 55-65 mph I get a vibration and noise coming from somewhere under the hood. It's not a very loud vibration or noise, but enough to hear. This only happens when I am going the said speed and SLIGHTLY pressing on the accelerator. It doesn't happen if I am going the speed and not pressing on the accelerator, or have my foot in the pedal. It happens at the speed with apprx. 1/4" to 1" of acceleration There are no fault codes and no loss of power issues to speak of. The truck only has 69,000 miles on it and runs great, but the vibration and noise is starting to get on my nerves. Any help or ideas would be appreciated. Thanks!

Is that an auto.trans? Gasoline engine?
2wd?

Gas , 2WD, Automatic

55-65 seems like an appropriate speed for the torque converter lockup to engage and for the transmission to shift into overdrive. A big engine like a 5.9 V8 I'm guessing runs at a pretty low RPM in overdrive. Applying the throttle at low RPMs would cause any engine to have a tendency toward what you're describing. The difference is in the engine and transmission mounts. I'm guessing they're not new.
Under the circumstances you've described, I'm not at all surprised that there's a vibration as long as it's not intense enough to shake bits of the truck off (interior trim, body panels, etc.). Your truck is 18 years old, so unless you're interested in replacing all of the engine and transmission mounts, you may just have to get used to a slight vibration when you first hit overdrive. A good way to test my theory is to shut the overdrive off (if you can) and see if this vibration still happens. If not, you have your answer. I just wouldn't recommend driving with the overdrive off full time, you'll wind up spending a fortune on gas.

That sounds like a good starting place.