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Exam 1 Solution

# Exam 1 Solution - EML 4312 Spring 2011 Test 1 Show ALL your...

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Unformatted text preview: EML 4312 Spring 2011 Test 1 Show ALL your work. Unjustiﬁed answers receive no credit. 1. Determine the inverse Laplace transform for the following problems (i.e., determine \$905))- 0 a. (20 points) . 1 , 17(3) — 8(8+ 1)2 o b. (20 points) 1 Y“) — 3(32 + 23 + 2) “B C [Co’i's ’g’ of \,(§) :— 2“ qt "3’34 4 E3732 CM?Q6~F we. ( ; 52 ,, 3A 533-5 «they; ﬁles-H.377 :5 S?"’g {3:2, \l)(+3 i @H 2 X '3 “l 1C { SCSJﬁSZ 5:" 0?” A i - .é: (A (we ”“5““ * Q 3; {SW \ _' .5 8 5:4 '- st «6 -Eé’l» J 5 i ‘ : 3 I "i V [43: i ,fe _ e (5“ \$5? l A 'EMC : if; _‘( ”8-H W _ '54 6H)?“ s a. é(@~m1+1\ i 2 \ 3’5 4. CS —‘ i __ if :34 ’L' A: 2 1/2 (S aerwﬁh/Z A? l \ ’5; .. 2 (@5305) +673)?“ (BX-i531 + (CABS ’r ' - E: vV/L .. _{ _£ ‘ (3 C7— "\ \/(:+\~ Va *if&e Co£€>+€ 5‘“ 'H 2. (5 points) Determine the Impulse AND Step response of the following system Y(s) = ___1__ R<s> <s+1><s+2> 9136‘; (5 points) If possible, -pp1 the ﬁnal va ue theore to determine 'y(t = 00) for both the impulse and stee input. If not possible or t '5 example, explain Why. - \ lA “B we» Vtﬁ’W'E'P—g/Z A+J 3. (10 points) Determine the output Y(s) for the following block diagram. 9 \$12.33 (W M3 \I = A6 WW MMA “Mal \ , A? .. 3%me Mar MM _ s w 1‘— WW Tncecﬂvﬁ —~ [0 “1341’" 4. (25 points) Draw the Root Locus for each of the following open—loop plants. You should Show your work on all calculations required to draw the root locus. For these plots, _ I do not require you to determine the breakaway points or where the plot crosses the imaginary axis. . A) @1909) = (\$159221?) [Fl- [gag . B 1 3 \$ﬂ3 Yr lol‘ 0 > 7 7 010(8) % W fl) ,, 1 023(5) = m 2&5 ”1D 5. (9 points) For each of the open-loop plants in Question #4, qualitatively describe (e. g., small K, large K, no K, all K, etc.) for What values of K Will the system be stable? 6. (6 points) Give three bullets that deﬁne stability — a full sentence is not required. at M\ d WM ‘3‘?" 2?” Z Pb ...
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Exam 1 Solution - EML 4312 Spring 2011 Test 1 Show ALL your...

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