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The difference in the Potential energies between two arbitrary positions downward displacements X1 and X2. (X2 > X1)
$$\frac{1}{2}k[x1 - x2]^2$$
$$\frac{1}{2}k[(x2)^2 - (x1)^2]$$
$$\frac{1}{2}k[(x1)^2 - (x2)^2]$$
$$\frac{1}{2}k[x1 - x2]$$
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