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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 560
    :height: 240


.. _RefImage_Object_1.svg:


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

Link stiffness: :math:`k\mathrm{=}{28.10}^{3}{\mathit{N.m}}^{\mathrm{-}1}`

2 cases:


* :math:`{k}_{1}=k/10`, :math:`{k}_{2}=\mathrm{10k}`


* :math:`{k}_{1}=\mathrm{10k}`, :math:`{k}_{2}=k/10`

Point mass: :math:`m=10\mathrm{kg}`

Unidirectional viscous damping: :math:`c\mathrm{=}50{\mathit{kg.s}}^{\mathrm{-}1}`


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

:math:`A` recessed end.

Force applied at the :math:`B` end: :math:`F(t)={F}_{0}\alpha (t)` with :math:`\{\begin{array}{}\alpha (t)=1\text{si}0\le t\le 1s\\ \alpha (t)=0\text{sinon}\end{array}`

and :math:`{F}_{0}\mathrm{=}\mathrm{5N}`.


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

The system is at rest at :math:`t=0`: :math:`u(0)=0` and :math:`\frac{\mathrm{du}}{\mathrm{dt}}(0)=0`