How to fix a jack plate when jack plate shakes when traveling up or down: start with removing dirt build-up on your jack plate.
The shake that occurs when the jack plate is traveling up or down is caused by dirt build-up. To prevent this from happening, run the plate all the way up and apply a generous amount of dish detergent, then run the jack plate down, and let it soak until the next time you take your boat out. The detergent will push the dirt out and keep your plate running smoothly.
If the problem persists, you may need to lubricate the jack plate. To lubricate the jack plate, use a non-oil or non-grease based lubricant such as a silicon spray.