Problem $5$

Problem $10\mathrm{.}3-4$ A cantilever beam $\backslash ($ A B $\backslash )$ of length $\backslash ($ L $\backslash )$ has a fixed support at $\backslash ($ A $\backslash )$ and a spring support at $\backslash ($ B $\backslash )($see figure$).$ The spring behaves in a linearly elastic manner with stiffness $\backslash ($ k $\backslash ).$

If a uniform load of intensity $\backslash ($ q $\backslash )$ acts on the beam, what is the downward displacement $\backslash (\backslash$delta$\_\{$B$\}\backslash )$ of end $\backslash ($ B $\backslash )$ of the beam? $($Use the second$-$order differential equation of the deflection curve, that is$,$ the bending$-$moment equation.$)$