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


Geometry
---------

The system is composed of a mass, a spring and a shock absorber. It admits a single degree of freedom in translation.


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


.. _RefImage_Object_1.svg:


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

Link stiffness: :math:`k\mathrm{=}{25.10}^{3}{\mathit{N.m}}^{\mathrm{-}1}`

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

Viscous damping:

:math:`c\mathrm{=}{c}_{\mathit{critique}}`; :math:`c\mathrm{=}\mathrm{0,01}{c}_{\mathit{critique}}`; :math:`c\mathrm{=}{10}^{\mathrm{-}5}{c}_{\mathit{critique}}`

with :math:`{c}_{\mathit{critique}}\mathrm{=}1000{\mathit{kg.s}}^{\mathrm{-}1}`


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

Recessed A end

Harmonic force following x at the resonance frequency at point :math:`B`:

:math:`F(t)\mathrm{=}{F}_{0}\mathrm{sin}(\omega t)` for :math:`t\mathrm{\ge }0` with :math:`{F}_{0}\mathrm{=}5N` and :math:`\omega \mathrm{=}\sqrt{\frac{k}{m}}\mathrm{=}50{\mathit{rad.s}}^{\mathrm{-}1}`.


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

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