M427K_Exam2B_Goddard_Fall2010

M427K_Exam2B_Goddard_Fall2010 - 4— i 5 “‘1’ N...

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Unformatted text preview: 4—; : * i 5/ ' “‘1’ N CONFIDENTIAL L M427K Exam 2B \ NO NOTES. NO CALCULATORS. ‘ 2 P ' ‘ ' ’ — r— 0 tered 1 Find the recurrence relation that generates the coefficients 1n tha sews solutmn to (ac + 2)}; 33; C311 5 A ‘ at 330 = D. t n E i3. 0 “WK d "9 fi— _. n "a ” M09119)“ X J ‘2' Zamx :9” Jr n _ §1é( *1 “HQ 36 (9%) 0” fit 1 (magmam ~—_ lag] x” = 13 1 amé-wa _ Elfinw‘témw 2% H) {m- 1} '2. (we ‘ZFCM-HXW 2. A 1 kg. mass stretches a spring 88.2 meters. The mass is set in motion by pulling it dOWfl 1 meters and releasing it. There is no damping. An external foroe equal to 6 5 position of the mass at time t. (I _L 9+ s “Wa- r"+ Fez-o a. t) is also apiaiied to the fiass. Find as function giving the HP Sgolsmég fluirosvgf fr, .4 i _L 1 “a? amasgé wulsmfiésew ‘R ‘l 7"}; ‘ I ‘ (39:53 9%- < $113 thfit’iBQ (x435) ma (14“?) {A 3. Show that z = 3 is a. regular singular point of (st:2 — 9)y” + fiy’ + my 2 0, and then find the corresponding indicial . e uation. . q iff‘d}@flig/w 1"“ 1L - 9 / Qg—JXHE) “ W Qifif _ a l _ r“ m @321 (a (Hf-<32“ Gaian r ‘ a 93% 2 {My - 6 fi «6’ P6 1 “If Mr“ *" ( _ 1 mpg *‘ _, r“? i flQ+r4)(n+r)afl@3) £30” flnwjaq +ég(m+r)gflxnghgflwjmi r a” A x _ E “W aw H" m w 9(01 +r+{)(n+rfl)aqflk .9}; @(n wwaflflk + *iiafi-fi r Hogaqg fi2£t{3 ‘iftsioortES s11.” . Express f (t) in terms of unit step functions and then find if” { f 03)}. 15 —15 f L, + Elf : 35 Z 9 ('7. 5. Use Laplace transforms ’50 301% the NP 3;” — SLY ' a) # Em "" 7M}; (1 .32; 5‘": f 4 +64%) @‘wcsmo : 'l =cos y(U)=D,y’(D)=UA f . _ 5 . U '9' t: "" 51H ##3##: £0 + ccs+v<sw w<s+gxga+9 | : AS3-tI4-3 —1- 852’- $ (-81% Cs +~ 131+ 1,; ' DEL} DE — ZIPS-2d 10 ' gel-J: (+0) 7—53“, 3%+0-%¢)t5 \ EQDJEZL—léz: Q (*qmfl r299 :{g gimmic fl50+6CTZC-ZD=Q “*9 I [_O(T_‘:f00 Mom ‘ w 1+: “M 74—qu 20%: ...
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M427K_Exam2B_Goddard_Fall2010 - 4— i 5 “‘1’ N...

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