Example $(10$ points$)$ The system consists of a beam with mass $M,$ which is held by a linear spring with the stiffness $c.$ The spring is pre$-$stressed so that static equilibrium is observed for $=0.$ The mass $m$ has the velocity $v_0$ at the time instant $t_0$ and its position is defined by the height $h.$ It falls down on the beam and a totally plastic impact is assumed. The spring remains always vertical.

Given:

$l=0,6m$

$c=313kg{s}^{-2}$

$M=2,8kg$

$g=9,81m{s}^{-2}$

$m=2,8kg$

$v_0=8m{s}^{-1}$

Insert the correct solution at an accurracy of four significant numbers into the corresponding fields:

a$)$ Evaluate the angular momentum with respect to the point of the left bearing of the system directly before the impact. $(2$ points$)$

$L=,[kg{m}^2{s}^{-1}]$

b$)$ Evaluate the energy of the system direcly before the impact for the displayed mullniveau. $(6$ points$)$

$E=,[kg{m}^2{s}^{-2}]$

c$)$ Evaluate the velocity of the mass $m$ directly before the impact. $(2$ points$)$

$v_1^{\text{'}},[m{s}^{-1}]$