1. Reference issues

1.1. Geometry

	The system with 1 degree of freedom is of the mass \(M\) type at the end of a spring of stiffness \(K\) oriented in the vertical direction \(z\).

1.2. Material properties

Spring stiffness \(K\): \(36.{\pi }^{2}N\mathrm{/}m\)

Point mass \(M\): \(1\mathit{kg}\)

The values are chosen so as to have a natural pulsation of the mass-spring system \({\omega }_{0}\) such that:

\({\omega }_{0}\mathrm{=}6.\pi \mathit{rad}\mathrm{/}s\) because \({{\omega }_{0}}^{2}\mathrm{=}K\mathrm{/}M\).

1.3. Geometric characteristics

The movement is done in the vertical direction \(z\).

1.4. Boundary conditions and loads

The base of the spring is embedded, the only degree of freedom is therefore the following movement \(z\) of the point mass M which is fixed to the other end of the spring.

The imposed load is a vertical sinusoidal force \(F(t)\) imposed on the point mass M:

\(F(t)=\mathrm{sin}(\mathrm{1,1}\mathrm{.}{\omega }_{0}\mathrm{.}t)\).

1.5. Initial conditions

The system is initially at rest.