{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam1_solutions - ME 391 FALL 2007 EXAM 1 WEDNESDAY NAME...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME 391: FALL 2007 EXAM 1: WEDNESDAY OCT 10, 2007 NAME: 50LUTlONF-C PID Note: i. There are 5 questions with equal weight (Total: 100 points) ii. A table of Laplace transforms has been attached at the end for use in questions 4 and 5. iii. Use of calculators is not allowed. iv. Only one page (8.5 ” x 11 ”, both sides) of notes is allowed. v. Please show your work in clear and logical steps in order to get partial credit. 1. Solve the following linear, first—order differential equation by finding the integrating factor. 2. The angle of twist (9(2‘) of a circular shaft subject to a torque T is given by the following linear, constant coefficient, homogeneous, second order differential equation 2 d 26+ci€+k0=0 dt dt where I is the moment of inertia, c and k are the constants of proportionality for the clamping and elastic torques, respectively. Given 1:20, c=4 and k=1, solve the above differential equation to find an expression for the angle of twist 0(2‘) . Your answer should have two arbitrary constants. I lot/£0 it Come + [email protected]:o —— J ILTZ—OJ (LE—Le) k1, 0&1 &£ 200W. u0g+ 9.0 alt? 0M: ZOM’L-l—Ltm—klzo m: ~l+i HQ- Mac/1m _L,+ oat. 2X20 — lea UL 3. Find a particular solution of the following differential equation by the method of undetermined coefficients y'+3y'+ 2y = e” Ci‘ w1+3m+220 x yczC,Q +C‘2Q__x ABYW 7’2 : AGEX lhoauwa v‘» m 6a W oily/Qty? Subxiw‘l-Mmy 5n W 09;; _x - ‘ FLAG. +AXQ“ +36AQ~XAAX2~Xj‘€ZAXQ'—x ~ Q’X -X — A2 +MK'WX’fZfi/JX :2“ a) All 4. Determine fm=r1{ 3s+10 } s2 +12s+100 W W! fzflzj‘ Hoo : S? {42; +26+61r ~ (§+6)Z+g? Fm LaP£OCQ Tmféw Tag/23 (f {Qafcfiktjébj Q:*6/ kt—A) K 1 § em‘flw H] 2 Qr—a)‘+ k1 211:, ; A 0w + 9 5’ 51" \ZS*1°° @6‘)2+ 8’2 €+6)24?l ’?;+\o : ACMKJ +83 s A =3 5° [0 m+8§ :3 E? 5—2A 2,; L; 25+“) : 2‘ 5+6 _ 3 52—;‘15‘41470 é+g)2+a>2 é+gji+gz ferf'lé 25445 : g f" 3+6 j‘k 51 52mm“? 66”)“31f fl géwmf 5. Solve the following initial value problem by taking the Laplace Transform of the equation, solving for Y(s) and taking inverse Laplace transform to find y(t). y’+9y = t+cos3t+cos2t,y(0) =1,y'(0) = 3 TalH—r7 Lapfioae TWAW 0% We $2an 5327"} *qofé7jiafi‘chri’écoS3’ff whorze) Fm Tfimfin W) {52 y(5) #5 ’yr(o):) + q 7. L + S + 5 52 ;Z_(q SZ+LP $178J-—S~—3 +<3VQ7 2 4“? r + 5? S‘Z‘t‘i J‘Z—t-L, 2 Q *qJVCV‘) 7. §+ 3 .9 I + I + I 52 S‘z—f? 52A,, jfffir) : 5‘ +, 43 \ 52+? $z+q 4b 1 2 4' S + I ,_ 5‘ («MW @149)" €2+L)G?+4/ Fm W, I4é2£.}:,Qakt q IJg,5 j: cmgt 52”” 5%?" 1"? 9L j: 5M.Bt g i4 3 ,\Lm\3t $24kz 574-31}— f k3 : k‘t—L'hkt ZEUHG) ,t l 3 Q f E _—L-’}: J—-¥'é 3 i I 3% —& 2t 6014‘?) 33 $201+?) “ 9:7 ( m J i"; Mr }: emu h1)1 5'1} .3334 5 Z L {(29); : L,’c9vn3t €7.44?! )2 6*?1)1 6‘ ,1 1 of f M T cowt , cabt Ghawuw qfé152j: ( Q ’HPXS “31/ 31,27— 62+21/(;?437')j : LCC/OSZ’C’CdSEt) 5 jec): fféYGJJ 1&5 3+1" 2 of" _L “' ' 2+4 34%; + EIZOme‘Li { j f+<3€J A“, 51+3lj(y%8/j €2+qjl : C033{ AQMxEt _L ~ 417 (N Jawhrj +%£s.xn3(: +§Lfcm2t~1w 36) 13 k3 kt—sin kt I— 14 2k3 sin kt—ktcos kt l— 15 2ks tsin kt I— 16 ZkSZ sin kt + ktcos kt I— 17 (b2_a2)s 2 2 cosat—cosbt Some Important Theorems 73m» = s2F<s> — sf(0) — f’(0) Z{e"’f(t)}=F(s-a) I{f(t—a)u(t—a)}=e"“F(s) ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern