Hello and welcome to Just Answer! I will do my best to help you fix your automotive problem today.
It will only do the vibration @20 mph and above and you can make it go away by turning left it sounds like a driveline vibration. Likley caused by a u-joint or wheel bearing. Is your truck 4x4?
Ok you could remove your belt so the water pump doesn't turn and see if the vibration is gone. But you can't run it long since you have no coolant flow.