Problem $6\mathrm{.}4$

i$)$ Obtain the equilibrium positions $x_{i,eq},i=1,2$ for the mechanical system braced against immobile walls, a distance $w$ apart, with $w{l}_1+l_2+l,$ shown in Figure $1.$

ii$)$ Obtain the transfer functions $x_i\frac{s}{U}(s)$ bdtween the force applied on the first cart, and the deviations away from the equilibrium positions.

$1$