{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test 2 spring 07

# test 2 spring 07 - NAME#1 Recitation Instructor_———...

This preview shows pages 1–10. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: NAME #1 Recitation Instructor _____.____——— Signature __________.. Recitation Time Elementary Differential Equations Math 240, Spring 2007 Second Examination, March 13, 2007 Show all your work in the space under each question. Please write legibly and organize your solutions in a logical and coherent form; answers which are illegible or confusing will not receive credit. Each problem is worth 10 points. 1. Find the general solution. 2y” — 719' + 33/ = 0 307170 law @043 ivy—9:0 we 30:}. \l A’ (ﬂdﬂk tail“ 2. Find the general solution to the system of equations. 9%Uid—V02g slﬂ '1 3+” {5% “7% iii, \$ij - , Aim?” 7’1? 9% “31%. 10¢ x N7 an?» ‘%% “67x10 O\7’7\ _ a __ \ Kg; 753% \07k «9 DL’ 3b “we QQ—ZﬂKDALﬂ :b arc we: 98* Jr L16 , a?” — )C ,‘H' 1 6+ \) ’l’bﬁ 27" %C\€6 ,LLQ/ .- ’Z/C\& - ~"Ur x)? \ﬁgéﬁ ~3L~Vﬂ 3. Find the general solution. 3;” + 4y = 3x2 ¥f%uvo Evilk \%;<ﬂu»1%xralaM2¢\ hﬂ 9&4w3x6»xc 93>2\$v\%ﬁ 8931“ LIX 4. UMMCL¥ {37x 4 a» 2378” LHHF*HB#%1A4QL23¢— quB ugco 7)\VALPLD a» (wax w Lamaze AC*% L‘% 4. A mass of 2 kg causes a spring to stretch 9.8m. This is attached to a damping mechanism with damping constant 5 The mass is allowed to come to equilibrium and is then set into motion by displacing it 3m and releasing it. Find the function a:(t) which gives the position of the mass at time t. ”‘ my ﬁAL ‘ ammo» \A<«\$\ a 7” \4 158%70 iuio NOV?» who 71?” +emLz O i \3 Lo WA :0 are [L 5. Find the general solution. CD7” «1% WW \: 0 mm + AWN m b 1 1J—nglx «11 “LY - \)2L\@ 4 (do J< LgLosu JV “W14: 6. Find the general solution. 1+e (fab nab {0 +\\k\om:o D—xx my; \jh: (4 Qj\ AV Lia/17k W Ta} 1 2\%\1+a\— a“ ﬁrm w“ u 2 6* MgﬂﬂfM-Z’ gw*/L (W \AAA H—Ux ‘— 45* \0}5\’H03L\ “in m — \ogmhaﬁ 2 a? \%\ HEW "éb 93“ WagVH 6 \\ (1r 43 a?» aﬁef’k + (o"‘+eﬁ°”‘\ MMHM 7. A mass of 1 kg is attached to a spring with spring constant 1 5:%. After coming to equilibrium, the mass is set into motion with a variable force of cost N, but is not given any initial displacement or velocity. There is no damping. Find the function :c(t) which gives the position of the mass attimet. K Pa \$W¥ic-ont sumac \$Mm20 5 . ‘ (Ll DLHCO A 0:)L‘k 74“: g Lost +LLQMY‘ 74g): Log’l *l’ Xﬁck%&%MPMﬂlWW%l®UMf N9“ 3 ’Pxérpl/ '* Premier l M l—wstl Jr 8 L054: Jr 1% cost + Rt L» \$9608 : ~7/Jx QVWC J'le cost *le LBS/C "Rt mid 9U 7km 1 owe): 3% £19;th +50 gut O”; MMZM Wm) 7km? LLSVWE 4 at wt Whip-o: (“inset % item % Lﬁmgk Q ~— 70(0ﬂ2w MALWM) 3 iltl" Khaki 8. A mass of 6199 is attached to a spring with constant 8 There is no damping. The mass is set into motion with an initial displacement of 2m and an initial velocity. It is observed that the amplitude of the resulting motion is 5m. What was the initial veolcity? 9. Consider the differential equation describing a mass-spring—damping system. 1 x" + 013' + Ex = F0 cos wt, 33(0) = 1, x'(0) = —— (a) Suppose F0 = 0. For which values of c is this critically damped? >4" >v L70 % A; \$10 U‘KMW W nevi/w LLALtlpmio 9”»‘vtlhl’l‘ro :2) C»\ (b) If F0 = 1 and c = 0 What values of a; cause resonance? 74“ “37k: nois waigqu a ‘PLW MW w‘/%/‘ (c) If F0 = 0 and c = 0, the solution is m(t) = 008% + x/gsin (You may assume this is true.) Write x(t) in theaform m(t) ﬂosﬁut — ¢) for some w and qb. x _ g); 025%; W/” 9; (gaugiqu so Loaf/L l" ggmg : (LAM \$0 U”\ \m’ﬁa PM Ch QW‘ 1 “E s “EEK FEM“— 7’3 3; US} , A i”? 95 wsgtﬁéwée \22/ Wist/k \ ’ Mi} 3\ 10. Match the graphs to the equations. Each graph ranges from 0 to 20 on the horizontal scale and from —10 to 10 on the vertical scale. (a) 2:” + 1033’ + 323 = 0 93(0) = 0, m’(0) = 100 b) as” + 16110 = 0 ar(0) = 0, x’(0) = 30 0) 5:5” + x’+10:c = 0 :r(0) = 0, x’(0) = 10 d) 1:” + 400:1: = 200 cos 18t 33(0) = 0, x’(0) = 0 e) x”+:r’+a:=cost 32(0) =0, 33’(0) =0 ( ( ( ( i I “\KXXTX‘KH‘E—h Nlrl rerl’VJl’lm'nlll I lia'lll This is the graph of equation (A . This is the graph of equation Cl . This is the graph of equation Q1 . This is the graph of equation This is the graph of equation C“ . ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern