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


Geometry
---------


.. image:: images/10000201000002B1000000BA6A48693DAB1E1B1E.png
    :width: 3.1201in
    :height: 0.8402in


.. _RefImage_10000201000002B1000000BA6A48693DAB1E1B1E.png:

The figure above is taken from [:ref:`bib1 <bib1>`].


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

**Beam:**

.. csv-table::

    "Stiffness", ":math:`{k}_{1}={10}^{7}` and :math:`{k}_{2}=1`"
    "Masses", ":math:`{m}_{1}={m}_{2}={m}_{3}=1`"



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

The problem is unidirectional according to :math:`x`.

The displacement of the first mass is imposed :math:`{u}_{1}=\mathrm{sin}({\omega }_{p}t)` with :math:`{\omega }_{p}=2.`.


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

The initial conditions are given by :math:`{u}_{2}(0)={\dot{u}}_{2}(0)={u}_{3}(0)={\dot{u}}_{3}(0)=0`