AK-MATH225F10-WS6

# AK-MATH225F10-WS6 - MATH225 Fall 2010 Name 6 Z Worksheet...

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Unformatted text preview: MATH225, Fall 2010 Name: 6 Z \ Worksheet 6 (4.4, 5.1) Section: D U ( 0'15 For full credit, you must Show all work and box answers. 1. Find the solutions of the given second—order differential equations. (a) 4y” + 8y 2 16 .. /; :. // LIML+OnW\$=O 7/254/7? O 7/) z : -2 ._ m=IE=IE|L ,6);Z/ 7f:,2 6% z git ; Q 04;; X) + as», (Ex) )W I. ,5; X " 7h:C1(o%(I-ZIX>+(&S;O(EX> X 1160:: j as”) 2% (b) yll+4yl+4y=e—2x +sin(2\$) X ,ZK v u L ' L : =7“ 1 U ’+» ' = "OZ" 7.; 75 + 17/, + ’75 O / 7A " 7" 7r _: L’ir’ L’iv" a ‘7,S’_:> m1 + L/mv” L} :0. ﬁWSWYZX) Lm+2l>a :0 mate/L6 ya mar—Z :ék/ix " " «5° 22: ' : w‘7. X > 'Z)‘ / Matt-1155 A L7H C: C + Clxg ﬂy? 5 ca Xlézx fﬂcos(l><) “IL 8‘57hﬁ'2x) 7F) : Zm x (“~2xe 'y'Z/iﬂ‘ﬁ (24‘) '- ~, +,z/5c955(2.><) L} ,7 /,/v , 'ZX K - ay 2 ~ yﬂazizva dexa%H-o<m+L/a: X . o . f Hﬂcasl‘gx? iﬁfﬁpﬁoézx) 42‘"izxw‘FWZhl/Acéﬁwyg9ﬂ +‘~/ a XMvazﬁj >nzw+28a\$12>ﬂ 1” LI WZXVL 4605(290'f EDS/‘4 [DJ] :, QWLX +570 (2x) 2* 'Z)( ’ . , g _ ’ZX \ a + ﬁecasaya —-<Msméax)~c +smza: 2.04 1 / 3/ {5 :0 _ ~ 7 : L 2. Solve the given initial-value problems. I _ Q r I/ - (a g%+2:—:=5e*9‘, y(0)=1, y/(0)=0 7f, , 7r _ 56/ 1X u I: van“ > aka 7h y}. +2jk / 7" 7f. 2x ,LL/dlx m +Zm +0 1X MCM43):O L‘ dc Y+ZKZ\$CLX : F6 (“1:0 / Mtv Va :9 D " °" -U ..,i ==§-c ‘ yhﬂé’é +C¢C d °6 / 7f - _ Day Z ;h3C4+CLC/Zx \CI +C/Z—C +§ / 7 / : VZ/CZéZX‘L Cu (‘0) 7” *ﬁy' 1‘9.) =0&& l 710, ‘ 175/ 7 too 0 l l ‘ - AX . l , 7H p 7hl+F7k +L’7H‘O/ ;A*C r o M?— + E”! +Ll :0 >739 : [14X+B) 5X :4XCX+54X Lm+LA me) ~o , :ACX+4an+BGX m:”“( / :'( (0 k: ¢;i”x+c2,é 7?” I cX+6L¢X+4XCK+BcK _C ,LIX C _)( Zﬂ¢x+4xé+88+5Lﬂcx+4X¢x+ch) 7— (C + La X +q (ﬂXK/X+,Igaxj\ :Xax [2.6- +8 + 56 Jr 5(5kaij + [4+ §H+Lh43 XCX /0 1:» -H ', 7’:"~1C,c x4,ch _: XCX J— )< )< 1 X \ + ’0 (“X’Lﬁé “1005/ V ' WHHOBéLD /OH:| ‘ 0):C+C ~12” I()—— - \L w +37 ~ 547—271 33% /L I Z 'q’B/V‘D'meﬁ/OVE‘TGB' 3T (5:507 C;:‘Cz_’ BQL :O , I i r C\:O CL:O ' ’ 1 x — P ’0 m)< 'W/ﬂr‘zzé" 7 1 1 3. Find the charge on the capacitor in an LRC series circuit when L = Z h, R = 20 Q, C = 3% f, E (t) = 0 V, q(0) = 4 C, and = 0 A. The following linear differetnial equation models the charge on the capacitor, q(t), at time t. d2 d 1 LJ +R—q + —C—q = E(t) dt2 dt 7,60): Ll/ £10);;’/0)=O ~17?”4«ZO)’+3002=O / + __ "1 7”+<ZO}’+IZDO7*O /}=7xzé ML +30”? “200:0 40: W 3301‘} léoo —- ‘ﬁwotH0:«co ~20 I “Coot 'ZO‘f : i : IKOF'éOC-FZQEC 7/ Li) :CI 6 + CLC 71°) (1:?qu 2 causal rib-é” 4.3% Ca;'(o —cot 1(4) = ~rom, ~ 20: I 7 V *6’01‘; +_ “2015 (,Jc) ~ ~24; (0a 4. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attache to t e spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) V m l 2. 7’ W Z F-Jifét) boy“ m;'ZiL/.C 225 t: ‘ L :LU) 3.1 = 1152) amt : éilw‘fb: & 5L] (:— éZiKCeSﬂltﬁlsh/‘ig _ 3t _ ~L ' ' ' "'" was“? m — :2: - 106% 7 «game waits/aw) a L>OH : T2" Z ): 'Zc, (fasted ’HCZZtthLfC) ’[email protected]&EF°LL'Q+W‘°‘Z 7(0): .=~\ / 7'10): -ZC.+‘~/C?,:O/ (492%. ='z’ (b) Find the equation of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of ZWS. (Use the convention that displacements measured below the equilibrium position are positive.) / ’ 2; -—r Z — LC, :7 -— l 7 (“*7 4507/ 7‘0) '51; f’ﬁ Z 760) _ a ' cpsCLiJC) tCLC 5 "ﬁt it) 7 ’Co) ; 'ZC, 7L Lice," “Z ( ‘flrﬂ : ‘ iZ’tC.aS(Lit)‘-€: Sl\o(LH,) (a) Write the second-order differential equation for y(t), the position of the mass at time, t, if the external force, f(t) = 10cos(wt). [‘4 // + b I + L : 17 ” + No £3,193,514 wt) .»_,,,....— (b) Find the solution such that w = 5 and y(0) = y'(0) = 0. 7U+léy :‘OC05[5Q 7F? 7,7l/t/Z97F: may“) 7;] 7L,” “(975:0 /7A=a’”‘5 7P>4cos(5t)+5em(3t) m?- + a so yf’ =—54s>n(sU +153ch 15%,) m1: - ((9 7f // : ~25 ‘GCOSZSH - LSBS’MZSO :‘f‘L, ‘ amt : 6%: : 'CQZLW‘ +2.5?!) (L: ~ ZS /lCoS/ 51% ) 4,5,8 s>né/:[//9::)[5f)+89a/SQ VB; C.Co§[")t> +C‘7/él00'li) 794;“) _ﬁ5:o o 7 :c, (05M 6) +Czsrn(q~t) +1030; Cosésﬂ A :53 5 :o “ 7/ :‘ig-CGS (5 t) 9/:«L1C, swat) Mapcoslwtwégswgvc) (0 :a 462:0 ’Co)=L£CL=o _f y 3 dab 7 c—Jfb /Xéb)' C: (c) Find the solutcihn such that y(0) = y’(0) = 0 and w =m4m- v “hat "phéﬁ'€1ffenon occurs at this value of w? 7 I + “’7 : [O‘OBMQ =c, (@SM‘U'I‘QsMZHéj 7h 1 G Cow/t) “97%) +5 i: stoUrO L+ ga “290W ’ Li (9‘0 L+c (Ln ‘ : *' C sln l" LCcﬁ / , “HQ ’ : IOCO bit) 7 ' 7F 7” 7” 5 +§Lsrmé Hawtwwt) 7P>9Cc5l r) l /M MAECALRS 2A7 :C) : O W = Aécolelt)‘/*6t\$l\n(%) 7/0) ;[email protected];O 77a} :ACaS ‘ L’A6\$)O(Ll{)+BSlDZL/ C-Z ’ O 7?, N; v 9qu Le t) ~Liﬂrsln/th) «w teas/Q0 7 U») : éfsmmj +H egosuﬁ) + H13¢95(L/L)~1(9BU70(L¢) » —? ASMZL/t) Wit) +3\$<Q9UId~lQ€7tﬁnéﬁg ( chmwm +19 W + 2 {OCOSUVO OFM ﬂfi (5&2? /ypr~étsro(wt-) W ...
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AK-MATH225F10-WS6 - MATH225 Fall 2010 Name 6 Z Worksheet...

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