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By inserting dampers into the outriggers, providing supplementary energy dissipation, further improvements in the dynamic response can be achieved. The aim of this study is to develop analytical methods for the dynamic response evaluation of a single\u2010damped\u2010outrigger system and determine the optimal outrigger locations and damper sizes to minimize response. Changes in the mode shape, damping, natural period and seismic response were studied parametrically using complex eigenvalue analysis of a continuous cantilever model, and the accuracy verified by comparison with a member\u2010by\u2010member model. A simplified single\u2010degree\u2010of\u2010freedom model was then constructed and studied using an assumed lateral displacement curve and the principle of virtual work. 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