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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 469
    :height: 141


.. _RefImage_Object_1.svg:


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

Link stiffness: :math:`{k}_{1}=4.{10}^{9}{\mathrm{N.m}}^{-1}`, :math:`{k}_{2}=5.33{10}^{8}{\mathrm{N.m}}^{-1}`

Point masses: :math:`{m}_{1}={10}^{6}\mathrm{kg}`, :math:`{m}_{2}={m}_{3}={12.10}^{6}\mathrm{kg}`

Unidirectional viscous damping: :math:`{C}_{1}=1.2566{10}^{6}{\mathrm{kg.s}}^{-1}`, :math:`{C}_{2}=9.0478{10}^{6}{\mathrm{kg.s}}^{-1}`


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

Completely free system.

Loading at point :math:`{P}_{3}` along the :math:`x` axis: :math:`F(t)0={F}_{0}\mathrm{sin}(\Omega t)` for :math:`t\ge 0` with :math:`{F}_{0}={5.10}^{4}N` and :math:`\Omega =19\pi {\mathrm{rad.s}}^{-1}`.


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

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