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Traditional tensegrity mechanisms are comprised of compressive (rigid rods) and tensile members (strings). Compliant tensegrity mechanisms (CoTM) introduce springs alongside strings and rods, allowing these structures to be more adaptable and robust. The kinematic and stability analyses of such mechanisms will facilitate better behavioral understanding for control of such structures. Generally, the kinematic analysis assumes zero-free length (ZFL) springs which facilitates simplification of equations of motion. However, a general ZFL does not exist and the relaxation of ZFL assumption for a CoTM introduces computational complexities resulting from their non-linear nature. The research considers equilibrium and stability analysis of a planar CoTM mechanism consisting of two triangular platforms connected by a compressive member and two spring elements. For an assumed numerical example, the analysis illustrates the increase in computation complexity, and non-linear behavior of equilibrium and stable solutions as assumption is relaxed from 1) both spring ZFL, to 2) one spring ZFL, and 3) no spring ZFL.