1. Reference problem#

1.1. Geometry#

The system diagram is shown in the following figure:

_images/10003C68000069D500005B2800C1BDD7955DD14B.svg

1.2. Material properties#

The properties of the material are as follows:

stiffness \(K\mathrm{:}4{\pi }^{2}N\mathrm{/}m\)

Mass \(M\mathrm{:}100\mathit{kg}\)

amortization \(C\mathrm{=}0.4\pi \mathit{Ns}\mathrm{/}m\)

1.3. Boundary conditions and loads#

The spring is embedded at one end and subjected to a \(F\) force at the free end. The point mass can only move in the direction \(x\).

1.4. Initial conditions#

At the initial moment, the mass is immobile and is in its equilibrium position.

\(x(0)\mathrm{=}0m\)

\(v(0)\mathrm{=}0m\mathrm{/}s\)