Reference problem
=====================


Geometry
---------

The system diagram is shown in the following figure:


.. image:: images/10003C68000069D500005B2800C1BDD7955DD14B.svg
    :width: 298
    :height: 254


.. _RefImage_10003C68000069D500005B2800C1BDD7955DD14B.svg:


Material properties
----------------------

The properties of the material are as follows:

stiffness :math:`K\mathrm{:}4{\pi }^{2}N\mathrm{/}m`

Mass :math:`M\mathrm{:}100\mathit{kg}`

amortization :math:`C\mathrm{=}0.4\pi \mathit{Ns}\mathrm{/}m`


Boundary conditions and loads
-------------------------------------

The spring is embedded at one end and subjected to a :math:`F` force at the free end. The point mass can only move in the direction :math:`x`.


Initial conditions
--------------------

At the initial moment, the mass is immobile and is in its equilibrium position.

:math:`x(0)\mathrm{=}0m`

:math:`v(0)\mathrm{=}0m\mathrm{/}s`