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


Geometry
---------


.. image:: images/100011200000298C0000094DFC99D4915D1C0F90.svg
    :width: 536
    :height: 120


.. _RefImage_100011200000298C0000094DFC99D4915D1C0F90.svg:


.. csv-table::

    "Point masses:", ":math:`{m}_{{P}_{1}}={m}_{{P}_{2}}={m}_{{P}_{3}}=\dots \dots ={m}_{{P}_{8}}=m`"
    "Link stiffness:", ":math:`{k}_{A{P}_{1}}={k}_{{P}_{1}{P}_{2}}={k}_{{P}_{2}{P}_{3}}=\dots \dots ={k}_{{P}_{8}B}=k`"
    "Viscous damping:", ":math:`{c}_{A{P}_{1}}\mathrm{=}{c}_{{P}_{1}{P}_{2}}\mathrm{=}{c}_{{P}_{2}{P}_{3}}\mathrm{=}\dots \dots \mathrm{=}{c}_{{P}_{8}B}\mathrm{=}c`"



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


.. csv-table::

    "Linear elastic translation spring", ":math:`k={10}^{5}N/m`"
    "Point mass", ":math:`m=10\mathrm{kg}`"
    "Unidirectional viscous damping", ":math:`c=50N/(m/s)`"



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

Boundary conditions: embedded :math:`A` and :math:`B` points (:math:`u=0`).

Loading: force concentrated at point :math:`{P}_{4}` in the form of a niche:


.. csv-table::

    "Point :math:`{P}_{4}` "," :math:`{F}_{{x}_{4}}=F(t)` "," :math:`0\le t\le \mathrm{1s}` "," :math:`F(t)=\mathrm{1N}`"
    "", "", ":math:`t>\mathrm{1s}` "," :math:`F(t)=0.`"
    "Other points :math:`{P}_{i}` "," :math:`{F}_{{x}_{i}}=0` ", ", ""



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

For :math:`t=0`, in every way, :math:`u=0` and :math:`\frac{\mathit{du}}{\mathit{dt}}\mathrm{=}0`.