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Excerpt
A stable position in which all forces are balanced (vector sum is zero) and the object of interest is not in motion.  Equilibria may be stable or unstable depending on whether the force acts back toward or away from the equilibrium position if the particle is slightly displaced from in.

Since the force at the equilibrium position is zero, the potential energy curve at the equilibrium will be horizontal.  This will be a local minimum or maximum, but is not necessarily global.  Hence there can be several equilibria as a particle moves along a line. 

Note that the net force must be zero.  In the case of the mass on a vertical spring the spring stretches from its equilibrium length to counter the effect of gravity. In the case of the mass between two springs both springs may be contracted or extended, so long as the force each exerts on the object is balanced by the force exerted by the other.

Add figures of force vs. displacement and potential energy vs. displacement.