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# quiz6b - 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 B Show all work; answers with insufﬁcient suppmt will not receive credit. GOOD LUCK! 1. Consider a uniform rod of length L with an initial temperature given by u(:v,0) = sin(7r:c/L), 0 S a: 5 L. Assume that both ends of the bar are insulated and a2 = 1. Find the temperature u(:1:, t). LQ = lex 196 ”(0,1): uxcL, {1:0 .1 IC- MUQM '-‘ 5””(15/ - I [8! “()0 {) : X0}! 775} wﬂ X;:)= X(L) =3 / , I X"! T “4711;, T.) XT‘ : X/T 2:) 7 '5 1? 3 ’A u‘) x"+ AX : 0 ((0 T’ .~. —/\T X75) 7 o X/(L/ :0 lrw ll) C') A :0 ”‘9 X” :9 =) X: 0X +1: Fro». )7 c at '= o :3 X :1 eigemﬁrc’ff” A: " 0 . X, t I E) A < a Let A z -— JA’ => Clorodeﬂlﬂ‘fc ear! '- f" x“ l 3 ° .. )0: ﬂ“): X(7l/=(, eﬂ1+ggﬂx X’: (”tie —c&,b‘.e :) C! —.-. (J :0 7f: eiﬁeyﬁnc/IIM ‘3 2‘ 7° Le+ 1“ lul- (horacftrifﬁl e411 . f-‘Lf/u XMU : (, C’J/U’X ?' Cf/P/MK x’ — ,c, MMXJr 4/11”?“ a. 7—D 7-) C :9 AL ’l/d :.) Cg“), I‘m/(”‘50 —c,,u,w AL + 9/169! ﬂt= a ,a; s 017! (ﬂ'r/ , J n‘T+ ”3 )‘w = ll: : '7}i (Hm. / K..= ("J "L! A, "49 =3 T, ‘9 =7 T: *4 _ WP __ ---f _ _ n’ﬂ‘ .- "’7'“ A?“ .1:- -') '1? T c) ‘I :1 eff{' LL t) (’3 1-K). I her. 4. ‘A M; .3: f 51 (n (9/ '2? = 7[(K) (a: ifL/(x/JX= .}f {7701 ZLCEZ L: (’ ’ ’ -> MT X'n-Z-i OJ 1" o L U' Ck : .E f [(K} 631%)(01 L = ‘1 L IL” .> ”79" 1 (NH/TI ( i Z- L (Wm L (71-! 7? L = “ '— l° — 7< + —— ( ——’— L (mm L (mm ° L. X o 2 I (—. (0.! (WHJR + v—l— (g(( -{ .1..— _ ..l_ (THUR CM)“ _ I1 )ﬁ + ?1+I/7( pkg/ﬂ (:i/LIMIZMIZJ ’ L5,“)?EX’L20 ' L. L L X - 5—,»: 1,) a 2. Consider an elastic string of length L = 4 whose ends are held ﬁxed. The string is set in motion from its equilibrium position with an initial velocity ut(:c, 0) = g(:1:). Suppose that a = 1 Find the displacement u(:z:, t) for x :OSx<1 9(\$)= 1 :1<:c<3 4—2: :3S\$<4 “it = “xx AC Ufa/f):u(4)-£; :0 Z'(‘ “(X/'7)='a. (@090) =8“; [9+ L1 5 XML] TIL‘). Ln?! XI?) : X(4., =9 T(o) :0 “if. "‘ka =9 XT” - X/ll- =1) "" ': l : -)\ K 'T ‘“ X ' )‘X =0 MD T”+ Mm um Tlnfo X(°l=¢>. X(4/'=> ‘l—wa (l) a) :9 Xﬂ=o :9 X :- 61+; / l;( =);p-D :) a=£:o 40“,“: C) 2‘79 Let )= Ml cknmoé'ym‘iz €714 _- I*+/a‘-=o X: (. (and): + gm MK K“ l Cl " ° =) r/wx/x-w 4/!»- )m C. to; 4m 4‘ gm: 4% '«o 1 ”r M Xr = If??? X ﬂ;(')’; .. All: [5 ...
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quiz6b - Math 415.01 Quiz 6 Name TA Younghwan Son Rec Time...

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