The Constant Stress Hanging String with Bottom Load - An Exact Solution

The unique solution for the fully stressed hanging string with a bottom load is found. For a given length of string, the problem depends on two parameters, representing the ratio of string density to maximum stress, and the ratio of bottom mass to maximum stress. The cross-sectional area of the string decays exponentially downward. Vibration frequencies are found from the exact characteristic equation. Results from analytic perturbation formulas compare well with those of numerical solution.