Consider a beam of unit length = 1 of constant bending stiffness c(x) = 1 with

Question:

Consider a beam of unit length ℓ = 1 of constant bending stiffness c(x) = 1 with two free ends.
(a) Determine, by direct integration two constraints that must be imposed on the external force f (,v) in order that there be an equilibrium solution.
(b) Can you relate your conditions to the Fredholm alternative?
(c) Write down a forcing function that satisfies both constraints, and then find all corresponding solutions to the beam equation.