Two response spectrum methods for the analysis of secondary systems had been suggested based on the complex modal analysis. The response spectra needed for both methods defined at the base of the primary system are used as the input. Both methods are applied to a 2-DOF secondary sFsten1 connected to a 6-DOF primary system. The mass and stiffness of the secondary system are chosen in such a way to have nine different cases. The coupled system is subjected to El Centro earthquake (May 18, 1940, component S00E). It is shown that the response spectrum methods are in a good agreement with the time history analysis. However, the conventional floor response spectrum method gives overestimated responses which may lead to overdesign. It is concluded that the response spectrum methods are sufficiently straight forward and efficient for design purposes since the time history solutions are uneconomical to start with and the use of several ground motions increases the cost rapidly.

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