N14 1998 Volvo vibration/shakes

Can be so many different reasons, but I would start with leveling valve and injectors

 

Then maybe see if driveshaft is out of balance or u joints are bad

 

Just had that happen to me last week(not for the first time).
I am not an expert but I would say it sounds like an injector going bad.
Finding which one it is, that might take a while but hopefully you can get it right.

 

Shakes is a broad term…

leveling valve or tire out of round would be a shake

injector would be a sputter that you would feel in the pedal with smoke out the stacks…

 

Not sure exactly what was your experience. However, on my truck, cummins n14 engine, whenever I shifted it into another gear, when I press the accelerator pedal, it would feel like it is shaking for about a second or two.
Right now, I will tell you exactly what was my experience as I don't wan't you to unnecesseraily spend time or money on a part that is good. Ok, so in my experience, an N14 failing injector can have few different symptoms. In my last case(not the first time it had happen), which sounds similar to what you're experiencing right now, whenever I would upshift OR downshift, AFTER I would press the accelerator pedal, the truck will shake for a second or two. To keep it simple, please give us more details as to what exactly happens while driving. I will do my best to help you out.
- I did eventually take the truck to my mechanic to replace the faulty injector, but that was after I found the failing injector.