simulate rope with mesh runtime

I wanted to try to simulate a rope with math. I have 2 vectors representing the ends, what do I have to do to make sure that the string is “taut” when the vectors move away from each other? and when they get close I should let the vertices of the mesh go down. Can anyone give me advice?

You can do it simplified:

If you want great results ASAP: buy an asset on the asset store:

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