The equation $$e_{total} = \frac{1}{2} k a^{2}$$ represents the elastic potential energy stored in a spring when it is compressed or stretched by a distance 'a' from its equilibrium position. In this formula, 'k' is the spring constant, indicating the stiffness of the spring, and 'a' is the displacement from the rest position. This relationship illustrates how potential energy is accumulated based on how far the spring is deformed, which is essential in understanding how springs work in various physical applications.
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