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A stability analysis is performed for the planar two-spring system using catastrophe theory. Basic elements of catastrophe theory are outlined and applied to the two-spring system to give catastrophe locus plots showing where a change in stability occurs. The method used for the two-spring yields a stability analysis without having to solve the inverse analysis. The inverse analysis for the two-spring system is used to illustrate system equilibrium positions before, during, and after a change in stability.

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