Elastic Potential Energy
Assuming an object attached to a spring that obeys Hooke's Law with the motion confined to the x direction, it is customary to choose the coordinates such that x = 0 when the object is in a position such that the spring is at its natural length. The force on the object from the spring is then:
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\begin
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[ \vec
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= - kx \hat
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]\end
It is also customary to make the assignment:
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\begin
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[ U(0) \equiv 0]\end
Thus, the potential can be defined:
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\begin
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[ U
= U(0) - \int_
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^
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(-kx)\:dx = \frac
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kx^
]\end
For an object moving under the influence of a spring only, the associated potential energy curve would then be:
POTENTIAL ENERGY CURVE
The graph indicates the presence of one stable equilibrium point at x = 0.