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


Calculation method
------------------

Here we treat a (almost) -one-dimensional structure problem subject to edge force, :math:`F(t)`, where the analytical solution can be written as,

:math:`u(x,t)={Q}_{0}\mathrm{cos}(Kx)\mathrm{sin}(\omega t)`

In order to obtain this solution, the force and the initial conditions specified above must be applied. The settings are also commented there.


Reference quantities and results
-----------------------------------

This is move :math:`x` to node :math:`A2` and right now, :math:`{t}_{\mathit{max}}=0.0012s`, which should be equal to

:math:`u({x}_{A\mathrm{2,}t})={Q}_{0}\mathrm{cos}(K{x}_{A2})\mathrm{sin}(\mathrm{\omega }{t}_{\mathit{max}})`

the value being calculated in the data file from the selected values of the parameters.


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

Exact solution.


Bibliographical references
---------------------------

S. Timoshenko, *Vibration Theory*, 1939