Vibration of Strings

Strings are basic structural elements that support only tension. They also approximate cables, with negligible bending, and chains, with numerous links. There seems to be no exact solution to the vibration of strings where the static shape deviates from a straight line. We assume that the tension, density, and deflection are continuous functions of position along the string, except perhaps at a single point in the interior span of the string. Thus, we limit our presentation to a string with at most two connected segments. For example, we include a string composed of two segments of different constant densities, but not multiple segments, since the solution of the latter can be extended similarly.