CONSERVATIVE LINEAR-MODELS FOR THE VIBRATING STRING AND ROD FREE TO SLIDE, AT ONE END-POINT, ON A VERTICAL GUIDE

The motion of a linear vibrating string, or rod, fixed in one point an d free to slide on a vertical guide in the other one, is studied. Only transversal vibrations are considered. The motion is simulated by a d iscrete conservative model. In order to prove that the total energy is conserved, a matrix form of the potential and kinetic energy is used. The same technique may be used to simplify the proof of energy conser vation theorem given by the authors in a previous paper. The numerical method related to the model turns out to be unconditionally stable. S ome examples of the motion simulated by the model are given.