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SignalsExam3SS04

# SignalsExam3SS04 - ECSE-2410 SIGNALS AND SYSTEMS SPRING...

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ECSE-2410 SIGNALS AND SYSTEMS SPRING 2004 Rensselaer Polytechnic Institute EXAM #3 (1 hour and 50 minutes) April 7, 2004 Check One: C Sect. 1 8:30am (Desrochers) C Sect. 2 10:00am (Wozny) NAME: __________________________________________ C Sect. 3 noon (Desrochers) Do all work on these sheets. Tables will be handed out separately. One page of crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values. Show all work for full credit. Total Grades for Exam: PART I 1 Grades for Points Score Part I 50 Part II 50 TOTAL 100 Problem Points Grade 1 5 2 7 3 7 4 7 5 12 6 8 4 TOTAL 50

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1(5). Express u(t) (3t) e 2 + u(t) (3t) e 4 = v(t) -t -t sin cos in the form of u(t) ) + t ( e A = v(t) t - θ ϖ α cos . v ( t ) = 2
2(7). Find the Laplace transform of the signal, else 0 1 < t < 1 - t + 1 = (t) x X ( s ) = 3

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3(7). Find x ( t ), the inverse transform of X(s) = 10 + 6s + s 2 + s 2 . x ( t ) = 4
4(7). Find x ( t ), the inverse Laplace transform of ) 2 + (s 3) + (s s = (s) X 2 . x ( t ) = 5

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5(12). A second-order system is described by x(t) = y(t) 6 + dt dy(t) K) + (8 + dt y(t) d 2 2 2 , where K is a constant. (a)(2). If K = 4, find the damping ratio, ζ . (b)(3). Find the range on K that will make the system underdamped. 6
Problem 5 (continued), (c)(7). Solve the differential equation when K = 0, x ( t ) is an impulse, 2 - = (0) y and 1 = y(0) . x(t) = y(t) 6 + dt dy(t) K) + (8 + dt y(t) d 2 2 2 7

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6(8). A certain linear system has the transfer function s/10) + (1 s/4) + (1 1 = H(s) .
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SignalsExam3SS04 - ECSE-2410 SIGNALS AND SYSTEMS SPRING...

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