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I have a bead of mass m, which slides down a frictionless parabolic wire in the form y=x^2, and is attached by elastic to the point (0,h), and I want to write down total energy f(x) (= elastic energy + gravitational potential energy) (no mention of kinetic energy...) of the bead at (x,x^2).

I know that g.p.e is mgx^2, and that elastic energy is (k/2)(h^2 + x^2 - 2hx^2 + x^4), but I'm not sure whether I'm adding the g.p.e. to the elastic energy, or subtracting it, despite the fact that I want f(x) = elastic energy + g.p.e.

Any clarification would be great :)

Thanks.