ON THE NATURAL MODES AND FREQUENCIES OF A SUSPENDED CHAIN

Abstract

Approximate expressions for the natural modes and frequencies of a uniform inextensible chain suspended from two points at the same level were obtained in a recent paper by Saxon and Cahn (1), who based their work on the solution of the fourth-order differential equation for the tangential displacement v. In the present paper the writer has obtained equivalent expressions using the angular displacement θ as independent variable. The differential equation for θ is of the second order, and was originally obtained by Routh (3) in a more general form for a non-uniform chain at least seventy years ago.