1. The problem statement, all variables and given/known data I need to find the distributed spring work over a beam connected to a ceiling. The position on any point on the beam is given by Z = h + σ*(x-x_ea). The spring constant is K. This is a wing model, where h is the plunge, alpha is the pitch, and x is a position on the chord. 2. Relevant equations Z = h + σ*(x-x_ea) Z_dot = h_dot + σ_dot*(x-x_ea) F = K*Z dZ = dh + dσ*(x-xea) 3. The attempt at a solution This seems like a simple question, but, is the potential energy differential for the wing dW = ∫K*Z*dz = ∫K*Z*(dh + dσ*(x-xea))dx or can it simply be dW = 1/2*K*Z^2dx ?