.. _V2.01.320:

**v2.01.320** SDLD320 - Transient response of a free system of 3 masses and 2 springs under harmonic excitation
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**Summary:**

We consider the transient analysis of a discrete linear mass/spring system with three completely free degrees of freedom. This system has non-proportional damping. Sinusoidal excitation is applied to one end of the system.

In this problem, we test, through a discrete model, the calculation of the transient response of a system whose rigid modes are not fixed. We are only interested in the transitional regime. To do this, the solution will be sought through integration on a complete modal basis.

The results obtained (displacement, speed and acceleration) are compared to an average of results from industrial codes and an improved :math:`\beta` -Newmark numerical integration method.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    Synth_se_des_r_sultats