Figure P9.20 shows a simply supported massless beam with a lumped mass at the center subjected to motions   (t) and   (t) at the two supports. Formulate the equation of motion governing the dynamic...

Figure P9.20 shows a simply supported massless beam with a lumped mass at the center subjected to motions
  (t) and
  (t) at the two supports. Formulate the equation of motion governing the dynamic component of displacement u (= total displacement − quasi-static displacement) of the lumped mass. Express this equation in terms of m, E I, L,
 (t), and
 (t).