Benchmark solution
=====================


Benchmark results
----------------------


* Accelerogram not centered


.. csv-table::

    ":math:`t=7.935` "," :math:`{a}_{\mathrm{max}}=–0.638` ", "", ""
    ":math:`f=100` "," :math:`\xi =0.01` ", "pseudo-absolute acceleration", ":math:`0.638\times 9.81=6.25878`"
    "", "", "Displacement", ":math:`0.638\times 9.81/{(2\pi \times 100)}^{2}=1.61607\mathrm{.}{10}^{-6}`"



* Centered accelerogram


.. csv-table::

    ":math:`t=3.1` "," :math:`{a}_{\mathrm{max}}=1.` ", "", ""
    ":math:`f=100\mathrm{Hz}` "," :math:`\xi =0.01` ", "pseudo-absolute acceleration", ":math:`1.`"



* Oscillator spectrum


.. csv-table::

    ":math:`f=0.5\mathrm{Hz}` "," :math:`\xi =0.01` ", "pseudo-absolute acceleration", ":math:`1.09558`"
    "", ":math:`\xi =0.05` ", "pseudo-absolute acceleration", ":math:`0.657348`"
    "", ":math:`\xi =0.1` ", "pseudo-absolute acceleration", ":math:`0.109558`"



Uncertainty about the solution
---------------------------

Analytical solution.


Bibliographical references
---------------------------


1. J.R. LEVESQUE, L. VIVAN, D. SELIGMANN "Seismic response by spectral method" [:ref:`R4.05.03 <R4.05.03>`].