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quiz6a - Math 415.01 Quiz 6 Name TA Younghwan Son Rec Time...

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Unformatted text preview: Math 415.01 Quiz 6 Name: _________________________ TA: Younghwan Son Rec. Time: _____________________ Form A Show all work; answers with insufficient support will not receive credit. GOOD LUCK! 1. Consider a bar 30 cm long that is made of a material for which a2 = 1 and whose ends are insulated. Suppose that the initial temperature is zero except for the interval 5 < :1: < 10, where the initial temperature is 20. Find the temperature u(:r, t). at = “xx B.c. (14(01): 11420, 75} = 0 IC- “(4,0) = l l0 JUN” 0 D'lkeruise . le’r amt; = XMUTH/ uHA X/(o) = x’raa) :9 “t = “xx => XT’ = XI'T =3 ~51 = Tl -,)\ go he Love (U x” + /\X=0 oi) T’=-}IT X’(:>):o K/(3°)'-‘-0 I Fwd) a) A=o =3 x”=o =) x: a“), Fth I3.C_ a =0 I Name x = i eigewfunc-fl'm I‘ow, X==l b) A<o . Le'l' ):../(,('l g CARMI‘I/Erll'I/I'c 67/! ")'}—,M‘l=o X00— Gel” +5941“ X’= (,fleMxfl(/4e"‘°‘ C) 1 A70 Le’r 2m,“ . dam‘fgflffi} 67;: Fargo XM) = Cl car/141+ CLJ'iV/Afl / X = —(,,u_ M ,u.)r+c;,0! COJflK Ac. => CUM—“*0. * 5 1:.) C :0 _ J/an/xto ” MU?” {aw/1L 6,41 M (emu =9 Hewe ”'9’” 3% 0'1' A = 37;: , W/ J, , r )v‘ “ -;>: XAMU = (a; 135:: 51mm} ADV—0 '9) TI = 0 :7 To =| Anrfl‘ 1-) T/ ‘ “A“; n’fl; 30;. -"";;:T 7') T:€)<f(""7-‘) “(XI i/ = C, + .2- e _ M 6 27M” %1} (01MB Fm If OJ % rill—Er a. C0} g"; WK) 70X) ‘2 3 /3 : )- - ‘i " ADD ‘ 3—20 )9 j. {max ” (Sf: WJX‘ "/J‘ u 3 ___ .2 1" m' l l” 7? (n z: [a 7/00 (oJ 3’99le " [—5- Jo (DJ(-:; K) 05‘ _ .10 an M ‘° 40 ' _ ,— _. -——x - :1 fl 1! 7m [rm{90 )1: h 7171 (M3 _. M 5) __ [0 a f: 1.71 __ 77 7P m M090 _ ’2— + Mi n (ma 3 my?) @271. ){aJ/ga x) 2. Consider an elastic string of length L = 2 whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(a:, 0) = f (11:). Suppose that a, = 1 Find the displacement u(:c,t) for z :Osx<1 f(7’r)_{2—:c:1sa:<2 “H - “xx Og XE; [H U(0,{) = ULLflé/ =0 ZC u (XI?) c {(X/ LL! (X,J) =0 lef a , KW! Tm um x0, =-X(_.L)=.o T’(o) =o // f .— X" T" ._ £11941»! 9 XT=XIl =9 7r-='.}‘-*)\ / A r . I P m X,+)X=D (w T/-+/\T=o UV” 1.5"" Xm=o thi=o Fur U) Q)):O X” :0 =) X¢0X+L )1 C =7 6 2’ :0 7..) a :J=o {Vii/ifil/ fa/A7/7'0M, 10+5=o b) )\<o Lei )=’M‘I CAGYfic‘Iér/Ffi} 69,4 V —,M2=o X* C,e“+ge"”9‘ lit. : c, +9 :0 j .11! =) (1‘: (J, =0 fiL/loj Ia [03703 C( e 4'98”” -0 C) A70 Le+ ); flll- CAWfic‘Ai’anIZ e9” f‘4 [a4 = o X = C. fsJ/MH Cami-2r fl-C 9-) C' : D 1 C, 0354,141— (LIMA/(=0 t> SMJ/‘l'flD 3/“ ‘ 77W (91' at, .i J I- arr Ar: ,un = 1477‘. X» = 5M (:X/ ...
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