Is it possible to animate objects along a path

Hi, I need to animate an object along a spiral. So far I found a workaround on how to rotate along a circle. Does anyone have a solution for animation along customized paths?
here is a simple file that can be edited:

Thank you for helping me out!

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I checked the file, the oval thing works, but the spiral one doesn’t work. Is there a way that something can be made to animate on the path?