Example $(12$ points$)$

A system, consisting of one rod with mass $m,$ is held by a linear

spring with stiffness $c.$ The spring is stress$-$free at $=0$ and

remains always horizontal.

Given:

$l=0,6m$

$c=60kg{s}^{-2}$

$g=9,81m{s}^{-2},m=1,3kg$

Insert the correct solution at an accurracy of four significant num$-$

bers into the corresponding fields:

Evaluate the derivative of the Lagrange functional $L$ with respect

to ${}^{}.(4$ points$)$

$\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}({}^{})}=,{}^{}[kg{m}^2{s}^{-1}]$

b$)$ Evaluate the derivative of the Lagrange functional $L$ with re$-$

spect to $$ for small deformations. $(4$ points$)$

$\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}}=,[kg{m}^2{s}^{-2}]$

c$)$ Evaluate the eigenfrequency of the system for small deforma$-$

tions. $(4$ points$)$

$=,[s^{-1}]$