General Energy conservation question

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Rock32
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This isn't really a homework question, so I'm hoping I can just get a straight answer from someone (although it is related to questions).

I realize that you can choose U = 0 anywhere you want in a gravity-related problem, ideally choosing a place where it is easiest to manipulate mgy values.

However, in a problem where both a spring force and gravity are of concern (i.e. where a spring is at an angle or hanging vertically), can you choose two different U = 0 positions?

That is, can you choose the lowest point to be Ugrav = 0 and the point where the spring is relaxed to be Uspring = 0, even if the two places are not the same y value? Or, do both PE's have to align?

Thanks.
 
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