Potential Energy for spring

?PEspring = -si?s Fspring? ds where Fspring = -kx

Recall that the minus sign in the PE equation comes from the fact that to store energy, we need to provide a force opposite that of the spring. This relation then gives:

?PEspring = -si?s -kx dx = ½kx2 - ½kxi2

If we choose xi to be the equilibrium position and call this zero, then we have:

PEspring= ½kx2

Note that this PE does depend on position (x).

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