Reference solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The reference solution is written for the degrees of freedom for node :math:`\mathit{N1}`:

:math:`\left(-{\omega }^{2}\left[\begin{array}{cccccc}10& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 10& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 10& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 10& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 10& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 10\end{array}\right]+\left[\begin{array}{cccccc}160& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 180& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 1280& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 180& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 1280& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 1960\end{array}\right]\right)x=0`


Benchmark results
----------------------

We get the following six pulses squared :math:`{\omega }_{i}^{2}` in :math:`{\text{rd.s}}^{-2}`: :math:`16`, :math:`18`, :math:`18`, :math:`128`, :math:`128`, :math:`196` in.

Hence the following frequencies: :math:`{f}_{i}=\frac{{\omega }_{i}}{2\pi }`


.. csv-table::

    "Mode", "Frequency (:math:`\mathit{Hz}`)"
    "1"," :math:`0.636619`"
    "2"," :math:`0.675237`"
    "3"," :math:`0.675237`"
    "4"," :math:`1.800633`"
    "5"," :math:`1.800633`"
    "6"," :math:`2.228169`"



Uncertainty about the solution
---------------------------

Analytical solution.