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Elastic force expression

Physics Asked on February 15, 2021

I would like to know how to properly write the elastic force in the classic x and y axes.
I know that the global formula is $vec{F_{el}}= -kvec{x}$, but sometimes the situation is little bit difficult. Here is an example of a situation where I struggle :

Considering here two elastic forces (springs of k coefficient and $L/2$ undeformed length) with the origin $O$ in the middle (A and B slide), for the "left" elastic force I write it this way : $vec{F_{el_A}}= -klsin(phi)vec{i}$ for the "right" one my guess is $vec{F_{el_B}}= -klsin(phi)vec{i}$ too. I do not know if I am right but the elastic energy says that $V_A(phi)=frac{1}{2}k(lsinphi)^2$ but $V_B(phi)=frac{1}{2}k(-lsinphi)^2$ which makes me think I was wrong for the forces.

Plane Oij

In general, how to write properly the elastic force and eventually elastic energy ?

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