ABSTRACT
The total energy of a string vibrating in a superposition of its normal modes is just the sum of the energies for the modes individually. As with the one-dimensional systems, the specification of boundary conditions—primarily, around the edges—limits the permissible motions to a few particular classes: the normal modes that are consistent with the stated boundary conditions. In particular, as far as mechanics proper is concerned, people can proceed from the analysis of the string to the vibrational behavior of almost any system that can be regarded as having a continuous structure. The study of vibrating strings has a long history. The reason is, of course, the musical use of stretched strings since time immemorial. Pythagoras is said to have observed how the division of a stretched string into two segments gave pleasing sounds if the lengths of those segments bore a numerically simple ratio.
