homework-05-solutions

# homework-05-solutions - ME 391 Homework 5 Assigned Apr 8...

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Unformatted text preview: ME 391 Homework 5 Assigned: Apr 8, 2011 Due: Apr 15, 2011 (34 pts + 10 extra credit) 5< Problem 1: Graph the following function and ﬁnd it’s Laplace Transform (smo f0%=_1 x34 SL5) 1 x>4 Problem 2: Solve using the Derivatives of Transforms: L{t2 cost} (5 PtS) ' P L S W3 r 26 (31’3> L<¢+03 % new awmkcvf‘ﬁ ‘5 F69 Problem 3: Solve by using Convolutions: L"{ 1 } s(s2+4) (5pts) 4‘ J“ JR L4 = ‘6 594 SCS +\ ﬁves) N Gen) :— Z' bwyz—f foo: , 303 X X ‘fﬁﬁﬂ “90’”ch “’ Y<§stxM0 EL 6 0' KA 1 21? «Pabsu> Prubfem 4a: Find AB and BAfor the foHowing twomatrices 1 2} '5 6 34 78 u z "5 V 1, Wﬁhu‘) lCo)~+ 21%)) f4 22. My. [:3 4H7 5] [Msﬂaﬁﬁ 3045403) ': 4g 57; ’ U ‘ I} “ [503% B) Say We“ 25 34 8”“ (:7 4 ' 10); 23(3) QCL)+3(4):[51 (“0] (9 pts) A =| 4b): What law does this represent? (1 pt) kg z}, BA CJAMMQTNTH/E No 0 Problem 5: Evaluate the determinant of the following matrix using the Cofactor 2 ‘1 ‘1' (10 pts) Expansion A= ‘3 2 l 5 O '2 M5? 1M Calvin“ because 0? a i ’2 + z (4)”; c ,- b deﬁ A: ’l CWHZ [5 t: "i ‘1 at k 2 (“Mai + 1(1) = E; 94 IRE-CALL COpACbeL is A Suave—m BEVE'MWWEVJT :) (0W L1“ is 81% Cu'chJ‘ 0AA Cy l =-.Mg Extra Credit: Solve the Linear System using Laplace (10pts) 1) y'+z = x 2) z'+4 y = 0 y(0) =1, z(0)='1 ‘ J. ® \$Y(S}%Wk '2(\$3:: s2. 5y(\$\+- 2(a): 27:44 sYCs'H- 2 Cs) 3 4-H 51.. (7? 32(5) *‘| k 4W5) =9‘ 57:93) * 4'y¢\$)=-( (Vf‘S) Et‘bucykoc‘. Mu: b‘ag): s’-\/ca\ +s%cs3 = 5 Cowbiwt~> 315/53 +51%) =- Sigﬂ > 3b- ‘ ’(4\/(.\$)A~ sir—(3) 2 .1) 5 Vs); 5?»:213 6:— 5ah S'qu 4g * as) C®] Wai— arWai WW2: " P 2M: X {2573 :- '53. 4‘1 “q .5. 4’ # 51(S,2A (ya) 3 67’ (IS-Z) (5&1) 63 3 3+c=( 6L: A—rlg" ZC.::"‘{r 1M3 «mg—4 ...
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