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# A#17 - Assignment#17 p.1 ECSE-2410 Signals Systems Spring...

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Assignment #17 – p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 03/31/09 Read Section 6.5 and Sections 9.1 through 9.7, skipping 9.2. 1(28). For the following, sketch the pole-zero plot, find n ω ξ , and determine if the system is undamped ( 0 = ) ζ or underdamped ( 1 0 ) < < or critically damped ( ) 1 = or overdamped ( ) 1 > . (a) () 4 4 1 2 + + = s s s H (b) () 5 4 5 7 2 + + = s s s H (c) () 1 20 1 2 + + = s s s H (d) () 5 4 5 7 2 3 1 + + + = s s s s H 2(16). The following pole-zero diagrams represent the transfer function, H ( s ) of four different systems (not related to the previous problem.) In each case find (a)(4) the damping factor (or damping ratio), , the (b)(4) natural frequency, n , the (c)(4) damped frequency, 2 1 ζω = n d . and answer the questions: for which of the four systems does the step response have the (d)(2) fastest rate of decay? (e)(2) highest frequency of oscillation? j 4 - j 4 -1 s -plane A -8 -1 - j 4 j 4 s -plane

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A#17 - Assignment#17 p.1 ECSE-2410 Signals Systems Spring...

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