\begin{definition}[Definition:Harmonic Potential Energy]
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'''.
\end{definition}