Reference issues ====================== Geometry --------- +------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------+ | |The system with 1 degree of freedom is of the mass :math:`M` type at the end of a spring of stiffness :math:`K` oriented in the vertical direction :math:`z`.| + .. image:: images/Shape1.gif + + | | | + + + | | | +------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------+ Material properties ---------------------- Spring stiffness :math:`K`: :math:`36.{\pi }^{2}N\mathrm{/}m` Point mass :math:`M`: :math:`1\mathit{kg}` The values are chosen so as to have a natural pulsation of the mass-spring system :math:`{\omega }_{0}` such that: :math:`{\omega }_{0}\mathrm{=}6.\pi \mathit{rad}\mathrm{/}s` because :math:`{{\omega }_{0}}^{2}\mathrm{=}K\mathrm{/}M`. Geometric characteristics ----------------------------- The movement is done in the vertical direction :math:`z`. Boundary conditions and loads ------------------------------------- The base of the spring is embedded, the only degree of freedom is therefore the following movement :math:`z` of the point mass M which is fixed to the other end of the spring. The imposed load is a vertical sinusoidal force :math:`F(t)` imposed on the point mass M: :math:`F(t)=\mathrm{sin}(\mathrm{1,1}\mathrm{.}{\omega }_{0}\mathrm{.}t)`. Initial conditions -------------------- The system is initially at rest.