Skill$-$Assessment Exercise

PROBLEM: Find the transfer function, G$)$s$)=x2\frac{s}{F}(s),$ for the translational mechanical systam chown in Figure

$\left[\begin{array}{c}\text{S}\text{u}\text{m}of\\ \text{i}\text{m}\text{p}\text{e}\text{d}\text{a}\text{n}\text{c}\text{e}\text{s}\\ \text{c}\text{o}\text{n}\text{n}\text{e}\text{c}\text{t}\text{e}\text{d}\\ to\text{t}\text{h}\text{e}\text{m}\text{o}\text{t}\text{i}\text{o}\text{n}\\ at{x}_1\end{array}\right]x_1(s)-\left[\begin{array}{c}\text{S}\text{u}\text{m}of\\ \text{i}\text{m}\text{p}\text{e}\text{d}\text{a}\text{n}\text{c}\text{e}\text{s}\\ \text{b}\text{e}\text{t}\text{w}\text{e}\text{e}\text{n}\\ x_1\text{a}\text{n}\text{d}{x}_2\end{array}\right]x_2(s)=\left[\begin{array}{c}\text{S}\text{u}\text{m}of\\ \text{a}\text{p}\text{p}\text{l}\text{i}\text{e}\text{d}\text{f}\text{o}\text{r}\text{c}\text{e}\text{s}\\ at{x}_1\end{array}\right]$

es $x{x}_1(s)+\left[\begin{array}{c}\text{S}\text{u}\text{m}of\\ \text{i}\text{m}\text{p}\text{e}\text{d}\text{a}\text{n}\text{c}\text{e}\text{s}\\ \text{c}\text{o}\text{n}\text{n}\text{e}\text{c}\text{t}\text{e}\text{d}\\ to\text{t}\text{h}\text{e}\text{m}\text{o}\text{t}\text{i}\text{o}\text{n}\\ at{x}_2\end{array}\right]x_2(s)=\left[\begin{array}{c}\text{S}\text{u}\text{m}of\\ \text{a}\text{p}\text{p}\text{l}\text{i}\text{e}\text{d}\text{f}\text{o}\text{r}\text{c}\text{e}\text{s}\\ at{x}_2\end{array}\right]$