A cantilevered beam with flexural rigidity $EI($and symmetric cross$-$section$)$ has a distributed load $q_o($force $/$length$)$ over half its span and is supported by a spring of stiffness k at its end. Assume the fit is perfect $($stress$-$free$)$ before $q_o$ is applied, and neglect the weight of the structure. Use potential energy minimization to find the field equations and boundary conditions.