Reference issues
======================


Geometry
---------

We consider a system with one degree of freedom, consisting of a point mass :math:`m`, 
a spring with a stiffness :math:`k` oriented along the axis :math:`x`, and a shock absorber. The movement is done along the :math:`x` axis.

.. image:: images/sdof.jpg
 :align: center
    :width: 100

.. _ref_image_sdof:

     Figure 1: Diagram of the mass-spring-shock absorber system.




Basic characteristics
-----------------------------

The mass is assumed to be :math:`m=1 \ \text{kg}`. The system's own period is assumed to be equal. 
to :math:`T=1 \ \text{s}`, which corresponds to a natural pulsation :math:`\omega_0 = 2\pi/T`, and therefore to a 
stiffness :math:`k = m \omega_0^2 = 2\pi \ \text{N}\cdot\text{s}^{-1}`. 

Consider depreciation :math:`c = 2 \xi \omega_0`, where :math:`\xi \in [0, 1[` refers to reduced depreciation 
of the system.


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

The base of the spring is embedded, the only degree of freedom is therefore the following movement :math:`x` of the point mass :math:`m` which is fixed to the other end of the spring.


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

We consider an initial displacement :math:`u_0 = 1.0 \ \text{m}` and an initial speed :math:`v_0 = 1.0 \ \text{m}\cdot\text{s}^{-1}`.