How are you wobbling them, with a script?
How about posting the script, or however you are getting them to wobble. If they are Anchored they shouldn’t move at all.
Maybe try adding a small block with an attachment in the middle that is anchored then adding an attachment in the plate and create a weld or constraint of some sort so the plate stays on the same position as the small block. I am just assuming you have created the “wobbly plate” by constraints, and not by scripts.
Are they still sinking since you mentioned that in your last post, but you marked @kaorukoSE’s post as the Solution.
If they are still sinking then try increasing the Forces in some of your Constraints.