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THE SYNTHESIS of a feedback control system is usually performed in terms of its frequency response, but system performance is best evaluated in terms of its transient response. Consequently, it is desirable to be able to relate transient response as directly as possible to frequency response. Although it is difficult to derive exact yet general mathematical relationships between these two responses, a great many reliable approximations can be found. This paper developed many of the most important of these approximations by examining and comparing the transient responses for a number of different types of feedback control transfer functions.