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


Geometry
---------


.. image:: images/1000055800000DF400000757BCE9867C7144ED7A.svg
    :width: 180
    :height: 80


.. _RefImage_1000055800000DF400000757BCE9867C7144ED7A.svg:

We are interested in the :math:`m` mass movement.


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


.. csv-table::

    "Point mass:", ":math:`m=1\mathrm{kg}`"
    "Elastic spring:", ":math:`k\mathrm{=}{\pi }^{2}N\mathrm{/}m`"


*Case 1*: conservative system (without amortization)

*Case 2*: dissipative system :math:`c=\mathrm{0,2}\pi \mathrm{N.s}/m`


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

The problem is one-dimensional in the :math:`x` direction, and in one degree of freedom: the movement of the :math:`m` mass.

The mass is left free, without external excitement.

Initially it is out of balance: the spring is stretched with an elongation of 1 meter.