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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 IRECALL 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 4H 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’ (ISZ) (5&1)
63 3 3+c=( 6L: A—rlg" ZC.::"‘{r
1M3 «mg—4 ...
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 Fall '11
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