$2\mathrm{.}2-7$ Two rigid bars, $\backslash ($ A B $\backslash )$ and $\backslash ($ C D $\backslash ),$ rest on a smooth horizontal surface $($see figure$).$ Bar $\backslash ($ A B $\backslash )$ is pivoted end $\backslash ($ A $\backslash ),$ and bar $\backslash ($ C D $\backslash )$ is pivoted at end $\backslash ($ D $\backslash ).$ The bars are connected to each other by two linearly elastic springs of stiffness $\backslash ($ k $\backslash ).$ Before the load $\backslash ($ P $\backslash )$ is applied, the lengths of the springs are such that the bars are parallel and the springs are without stress.

Derive a formula for the displacement $\backslash (\backslash$delta$\_\{$C$\}\backslash )$ at point $\backslash ($ C $\backslash )$ when the load $\backslash ($ P $\backslash )$ is acting near point $\backslash ($ B $\backslash )$ as shown. $($Assume that the bars rotate through very small angles under the action of the load $\backslash ($ P $\backslash ).)$

PROB. $2\mathrm{.}2-7$