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Unformatted text preview: 6.003 Homework 7 The following problems are intended to help you prepare for the upcoming exam. Please do them by Wednesday, October 28, 2009 . You need not submit your answers: they will NOT be graded. Solutions will be posted. Problems 1. Maximum gain For each of the following systems, find the frequency m for which the magnitude of the gain is greatest. a. 1 1 + s + s 2 b. s 1 + s + s 2 c. s 2 1 + s + s 2 Compare the m for these systems and explain qualitatively any similarities or differences. 2. Phase For a second-order system with poles at 1 and 4 (and no zeros), find the frequency at which the phase is 90 , using any method except for the vector method. Then illustrate and confirm that result using the vector method. 3. Matches The following plots show pole-zero diagrams, impulse responses, Bode magnitude plots, and Bode angle plots for six causal CT LTI systems. Determine which corresponds to which and fill in the following table. h ( t ) Magnitude Angle PZ diagram 1: PZ diagram 2: PZ diagram 3: PZ diagram 4: PZ diagram 5: PZ diagram 6: 6.003 Homework 7 / Fall 2009 2 Pole-zero diagram 1 Pole-zero diagram 2...
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- Spring '11