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How to animate wavy tail in material?

I would like to take my 2d tadpole creature/sprite and animate its’ tail in a material, which is currently straight(I want it wavy and moving/flowing naturally).
I have a mask with the tail in white and I’m thinking I need to combine this with some kind of gradient that can simulate a wavy tail using the sine or panner nodes or both?
Would it be better to create a flip book?
Update I managed to get what I was after with time, sine, panner and rotateaboutaxis nodes but turns out I lack the vertices for proper displacement.
I may use a higher res mesh to create flipbooks for the 2d sprites… Much to learn…