A general asymptotic solution to the linear dynamics of a taut inclined cable is derived. All known analytic solutions can be obtained as special cases, while it is demonstrated that the most important parameter is proportional to the product of the square of the local curvature and the elastic stiffness. At certain values of this parameter the distance between the natural frequencies of a symmetric and an antisymmetric mode is very small but they never coincide, while both modes become hybrid modes, a mixture of symmetric and antisymmetric shapes, with a significant effect on the dynamic tension.
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Michael S. Triantafyllou (1984) studied this question.