Use Hamilton's principle to derives the equation of motion and the boundary conditions for the flexible beam BC in Problem 12.4
Problem 12.4
A uniform, thin, rigid bar AB having mass M and length b is attached to a uniform flexible beam BC. Assume a small transverse displacement v(x, t). Using appropriate diagrams (free-body and kinematics), determine the boundary conditions for the beam at B and C, that is, at x = 0 and at x = L.
