Reference solution
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Calculation method
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**In the linear static case:**

:math:`{E}_{\mathit{pot}}={W}^{\mathit{ext}}=\frac{1}{2}{\sum }_{i\in N}{D}_{i}{F}_{i}^{\mathit{ext}}` where :math:`N` is the set of model nodes.

For a small model, it is therefore easy to calculate the potential energy from the displacements.

**In the case of modal calculation:**

If :math:`\Phi` is an eigenmode of the problem, of natural frequency :math:`f=\frac{\omega }{2\pi }`, with :math:`K` stiffness matrix of :math:`M` mass matrix then :math:`(K-{\omega }^{2}M)\Phi =0`, hence :math:`{\Phi }^{T}(K-{\omega }^{2}M)\Phi =0`.

If we norm the modes with respect to the mass matrix :math:`M` then we have :math:`{\Phi }^{T}K\Phi ={\omega }^{2}={(2\pi f)}^{2}`.

Gold :math:`{E}_{\mathit{pot}}=\frac{1}{2}{\Phi }^{T}K\Phi`. So all you have to do is check that :math:`{E}_{\mathit{pot}}=2{(\pi f)}^{2}`.


Reference quantities and results
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Uncertainties about the solution
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None.