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# Test3Solutions - - 7W? Math 306 — Test 3 Printed Name: -...

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Unformatted text preview: - 7W? Math 306 — Test 3 Printed Name: - i. Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit! The Printed Name question is worth 5 points. a H indicates a “By Hand” problem Where technology is not allowed. I '1? indicates a “Technology” problem where you {gay use Mathematica or a calculator. You must still 5 Show the steps taken. For example, f (1 ~— 11:)7 drv 2 —8,192 is valid. Giving the answer —S,192 without 1 the integral is not. 0 Do not use DSolve or NDSolve unless otherwise directed (except for checking your work). Use the deﬁnition of the Laplace Transform (not the tables!) to compute ,5? t j r" “5% n ‘ V‘ _ g to - 3 “’3” "Mg W ' “wife. l w 53 {it Hi L (if ('3 9 wﬁm L \f ' 0 {j ..: 0 2L "é‘ t _ V a: Q m g " T8 ‘ t: u —i: E . éiig git; ’ WW .3 g i O cited/z w l v ' ... Lav... “:3” “if” db A“... MJWWEH i» m ix?er if \$1 J i if 1 m éb {i > 0 ii 1 j E} ‘1 ,a—ww—W‘“ H 2 [220} 1”” Compute by hand (using reasonable means - tables, formulas) \${362‘ + 2 si112(5t)}. I ' ‘ W} m. Iiifiéfg~ l“€vj(l€ﬁf'21§g CCUQL'A' “2b ( > :Efm?€m‘}t {w agile} 1" .i —— wiiiolﬂ} "’ Dr. Emmert Spring 2010 I of III Points Earned i: of 30 Math 306 ~— Test 3 Consider the IV}) 51:” w?» (#83: = F0 cos(w0t), = 0 = m’(0) which models a mass-spring system that is undanlped. Use Laplace TI‘ELDSbe‘IllS to solve the initial value probiem. i I, ,. “" 335 ~ g E :M + Mm ~ m Wat‘s “Ia J]wa fowﬂ “M”: 335%} '2 E“ [\j h I ‘ I Caiculate linl L—POO . ’ Fa I m M “Mai (WI twinge) _ m9 Em)?” :- 2 “Jul + {>43 Sketch ‘Nhat type of phenomenon does this undamped system exhibit? 7K ‘ LE / gm“ . Points Earned 1:: of 40 II 01" HI Dr. Emmert Spring 2010 Math 306 — Test 3 25 _ 3 23 — 3 3 7 10 11m 0 t 3’1 — . t.‘ — 1 _ ' 011m“ B {(sw3)(3+2)} m (aw—3)(5+2) 5(u3 +s) {L 5(2+S) ‘ ~r y j,” I Wig émi 3 3k, «lf '3: e + f E: \, Find a nontrivial solution to the IVP m” + (t — 2)::3’ + a; = O, : sc’(D) = 0 using Laplace Transforms. ﬂ”? + ﬁégfmth’] nf’itxicﬁfvf—E H - 50 my"??? ﬁx} + {‘1‘}! {gig} n 2L Mix} My] +95th .5" :21} s -iw 5“! f —- m :m.~,. Emmi] Ml; Mwmax] C15“ m3 m1] 2 41 “ii I I JI'XEEEI " J‘ Kit-E’s] “‘ Ni”) +3”) “3 "[ 2mm igré’z’m] - [ 3(3) +‘r2’cpﬂ «24’ 2W“) +33?) :0 - (3‘1 Highs) ~ Wm: to (ﬂuiI’pr—ML’iC-i “X’a‘; : p LL? M mi! W x. , 3fo ‘3‘?- M” J“ i i wzmt : my? Hi, Dr. Emmert Spring 2010 III of III Points Earned i: of 30 ...
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## This note was uploaded on 01/16/2012 for the course MATH 306 taught by Professor Keithemmert during the Spring '11 term at Tarleton.

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Test3Solutions - - 7W? Math 306 — Test 3 Printed Name: -...

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