# Definition:Harmonic Potential Energy

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*This page is about Harmonic Potential Energy. For other uses, see Harmonic.*

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## Definition

Let $P$ be a physical particle.

Let its position $\map x t$ be a real function, where $t$ is time.

Let $k > 0$.

Then the potential energy of the form:

- $\map U x = \dfrac 1 2 k x^2$

is called the **harmonic potential energy**.

## Sources

- 1963: I.M. Gelfand and S.V. Fomin:
*Calculus of Variations*: $\S 4.23$: The Hamilton-Jacobi Equation. Jacobi's Theorem