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07m1-solution-yellow

# 07m1-solution-yellow - SA Midterm 1 Spring 2007 Instructor...

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Unformatted text preview: SA Midterm # 1 Spring 2007 April 27, 2007 Instructor: G1 Wei Name {if/0 ("l/j Discussion time (circle one): T811111; T413111; T513111; T613111; T7pm; 38am; R4pm; 3.513111; Rﬁpm; Your Scores: 1‘ ,,,,,,,,, 2‘ 3. 4‘ ......... 5.1 Your Total All questions have equal points" Continue on the back of the page if you need more space“ Good luck! in Solve the initial value problem. 11” — 411’ + 5y = 0, 11(0) = 1, y’(0) = 3. White your solution 111 the phase—amplitude £01m. The (1411 Fax/feyi'sh‘c 177442195” 231 f1.— oy+ 5-": 0 1 f m 4-w- “W _. 1 2. “2:1“ 9 (a £41. ﬂaw/(J fro/mam 2;; (70?): 621: (Cf £011" + C7, anf') 3(0): £( 3””! (le111) 1—, 25” (L, Mt+ £13715)+€Ll(~*c}{71f +(zdé’5f) 3'70): ‘26, +CL ll 3‘ 613/ W) t; C” (Mew-711— 2. Find the general solution of 2y”! W 3y]! + y] = O 711 C/fwa’ogwfrh‘c (fﬂwho‘h 7/} 3 I. may +r90 Y(lf1~3}’+f)r: r(_2,y...,-) (Ir-’1) \$0 7/112. WWW/(7 YO/Mﬁa‘u 21 L% gm :: a 413,6 -+ a; 6* 3‘ Find the general solution of yr: + 4y: + 4'9 z 8152“ 7A2, Mimi/avohw’r‘m «771641951: 2); ﬂaw/yaww DE 7% Vwr-w-w Ufa) :0 raw: rarmtlulg, ya "'3‘ C: Quilt + sz'ﬂdf 7’7 VI'SAf +8f+CJ 1%,“ grim zAf—r-(g {f 5,, m 2A+HLM+M+ ¢(ﬂfh+8f+c}:é’ft m=£ 4:2 Bz~' —- imwaw? I (f' Cl} 24+<H3ﬂ£cr~o f . ‘ MLE ~L 7'1}. WM ”ML—1,, 2:5 gm: m: axe, + Na“— H +3 4‘ a) Find the steady—state solution of the diﬁereutiai equation :12” + 4:1:’+ 33: = 20 cos it 33) Consider the differential equation y” + ay’ + 4y = 0‘ For what values of" a. Wiil the solution osciilate? q) fqu OKWVMjW/ffﬁlrc riflém D1l Aytwfww’wj DE 74 {1+ (FF +2 2.10 (MINI/H} 9:? I I”: 4/ ”’3 XL, 3 CI Cﬂf 4” C1. 6,5 Cu K! r A £451? + r} I’M" , MM KI] a: “/9 S"'Tnf”f(§€vﬁf Kr” :— - A Mfr” 81'7“? #4 Mi“ «4; KM + Hvﬂ mfﬂﬂ mfj-HMLM f/SIM) fzﬂHmf/w 32’9““— ;B “W? ”/0 L/ 7k III/M554. owﬂoﬁ M6344 dye Mmh me, whiff/X," New»? CZ‘L” (9% {.0 5. a) Find the motion of the mess—spring system with mass m 2 0.25 kg, spring constant I: = 4 newton/ meter and damping constant I; = 2 newton sec/meter“ The mass is initially pulled to the right, stretching the spring by O 1 meter, and then released vs ith veiocity of 0 ﬁrm/sec. b)At what time is the sprmg mmameﬂy stretched? M @gxeyh.defﬂﬁﬁ fwﬁ“ awrx +2x eex-po ‘Wﬁsoj Xﬁﬂgeg %rL%zr%¥=»0 rt+£Y-fw.ao (¥+¢)L :47 re”? ‘. - e _ «ﬁat Xejwﬂw ”+6 {Ewe ~10 . «ow/aw «.3; :gémywm X’H’) Cindy 7461” 7L 1: "‘ “L {“me 52:6, 76:1 (’ﬂlffl‘m/{y 72\$ 4 M ”U’Jffwug ﬂt 5/24”; 125 mu W (may, {£66.} (wad mh/f/o: ...
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07m1-solution-yellow - SA Midterm 1 Spring 2007 Instructor...

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