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I've been trying to solve a problem which i don't even know how to approach.

I have a vertical hanging cylindrical beam (free to swing sideways but not around itself), the beam is subjected to an eccentric load, downwards, at the bottom of it. The load is parallel to the swinging plane (it dose not create a torsion force in the beam).

I want to get to a parametric equation that can give me an approximation of the max deflection of the beam at the bottom.