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This paper presents a method to determine directly an acceleration response spectrum for a certain damping value when a response spectrum is known at the same location for a different damping value. This technique generates a response spectrum without having to apply any acceleration time history. For each frequency of the known response spectrum, the amount of response buildup and the number of cycles necessary to reach the peak acceleration are first calculated, and then evaluated to arrive at the response buildup for the unknown response spectrum. As a result, the peak acceleration for that frequency can be calculated. By repeating this process for each discrete frequency, the response spectrum for the required damping can be generated. Various acceleration response spectra are generated through the method presented here and are shown to be very close to those developed through the more expensive time-history technique. In addition, even if the acceleration time history is not available, the response spectrum for a required damping can be created provided that the response spectrum is known at the same location for another damping values.