A uniform road of cross section area A and length L has material properties E (Young's modulus) and p (mass per unit length). The rod is anchored at one end but has a forcing function Fosin wt at the other end. The governing partial differential equation is: d2u/dt2 = a2d2u/dx2
where u(x,t) is the longitudinal displacement and a2 = E/p
The boundary conditions are u(0,t) = 0 and du/dx(L,t) = 1/EA Fosin wt.
Determine the forced response u(x,t) by assuming u(x,t) = X(x) sin wt. Solve for X.