Abstract
We study a pole assignment problem by multiple-input state feedback control arising from a one dimensional vibrating system with aerodynamic effect. We derive explicit force terms which can reassign part of the spectrum to desired values while leaving the remaining spectrum unchanged. Unlike the classical Sturm-Liouville eigenvalue problem, the associated eigenvalueproblem is cubic in the eigenvalue variable and has new interesting math-ematical features. The spectrum of the associated noncompact operator is shown to be contained in the union of a real interval and a countable isolated set. This sheds light on the adjustment of model parameters.