When solving vibration problems of continuous systems such as bars, shafts, beams, etc., the displacements, W(x, t) were assumed as X(x)T(t). X(x) which is the mode-shape function is solved using what conditions?

Aflagpole broke in a storm. it was originally 8 1 81 feet tall. 2 8 28 feet are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground some distance away. how far away is the end of the pole from the base of the pole along the ground?