Homework3Solution

# Homework3Solution - Problem 2.6 1. Determine deformation...

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Unformatted text preview: Problem 2.6 1. Determine deformation and velocity at impact. u(0)=T£=—19-=02 in. k 50 am) = —1/2gh = ~1/2(386)(36 = ~166.7 in./scc 2. Determine the natural frequency. a) :f—kgz (swam 24393 rad/sec " w v 10 3. Compute the maximum defamation. L2(O) a) u(t) = u(0)cosa),,t + sina)": n = (0.2) cos 316.81 —- 1667 4393 J sin 316.8t 12(0)]2 uo z [u(0)]2 +[ 60 ﬂ :Jozz +(~-3.795)2 =3.8 in. 4. Compute the maximum acceleration. a", = wnzua = (43.93963) = 7334 in./sec2= 18.98g Problem 2.20 F 0.1w 0.1mg 0.1g 0.1g 11;; 2: -—- : ——~—- : -—-—-——— Z 2 z 2 k k k can (mm 2 mi = 0.0mm. (87!) The reduction in displacement amplitude per cycle is 4a,; = 0.244 in. The displacement amplitude after 6 cycles is 2.@ ~ 6 (0.244) = 2. t} —— 1.464 = 0&6 in. Motion stops at the end of the half cycle for which the displacement amplitude is less than uF. Displacement amplitude at the end of the 7th cycle is 0536 -— 0.244 = ' .; at the end of the 8th cycle it is 0.292 —— 0.244 x 0.948 in.“ . i . 0 504% i we ., gaps a? lee % Helm» WE: {Leta/VE Mil/291+ Svgmg \$41 A) ww/é: a) M): % C + k bk :1 0 5mm? Umgamm 2:355 :?27m% I My 3% (9.0m ‘ W {192: WWSM%t1 J}. i; 6 2? [095 523\$ 9223c +0233 3% \$21k] g” wag [Zaiﬁ gag wgé; ‘3’ z 5 A“ [0.545 {@aCazabmozmﬂ Le :M-ewé é .gi2?{g 6%; 23> «=6 : «\$.2‘?5Q4b%>§ 5&5 2’ {Vi aggﬁszﬁé (O 54.3 {:95 (322%???) 2 6:5 j) Raﬁ We; .. Q 92'? {213+i) 543 {\$53 277’) 2. a. 1%??? {a a??? W 4927 §*L“”:;:’€M(Qsié»8 O 4/ ‘Of ( O 2 ma ggé C. “ ’ ﬂfwwxmﬂq gzﬂim g. 3 (0&5 a}: (mg i. ﬁfggéﬁ- {#32 w @332) w 53/.le ‘f m a: /, 5? {4 ggmfgm 5:45? 5 ﬂ ﬂ @3555 (A) a 6m wk :2 C ” Q g; a '6 ,6) ' axggafmgﬂw w" 5‘5 Ca: JW ﬂag?) Fig“ 5 51?; £54931»; ‘5 * vaiif'ﬁ! ya :5 pm 3‘; 1v: )1 {335.32% 402. A ‘. . ) MX+C><H<><=O ﬁ€o§=02 . ﬁgs} 2 :3 3‘1 €9.93” '5? i“ j - né a“): (awées Wed; 4 Ed) 1%)) 3354 W 6):? SQ 5ft: “342355. {4:425} 7AM {0.12 £223 443%; + (\$.a355)0.2 \$444495}: Response Exp. Envelope 12 14 16 18 20 10 Time (sec) .\\..\\\\.\\ox.\\\.\v{o\\\ «Ax/III KKK‘R _ [fliiiiilllr ,_ .xixxxsxxxzxxlmv ,Ax i115? {14415.1 \EHV x‘xtksi Asiff: _ HHva if}? fff {£311} {UV AHMHHHMEE :33}; .... {plieihv E: illi‘lliliivt EV omcoawmm {3 C \Documents and Settings\Jerome Peter Lynch\My Documents\CEE Classes Teaching\CEESll Dynamicspage lork\I January 20, 2004 12:38:19 AM %CEE511 — Homework #3 Solution lProf. J. P. Lynch %University of Michigan % Problem 4: count = O; for t=O:0.0l:20 count = count + l; u(count) = (O.2*cos(4.48*t)+0.0355*O.2*Sin(4.48*t))*exp(-O.159*t); har(count) = (O.2*cos(4.48*t)+0.0355*O.2*sin(4.48*t)); env(count) = O.2*exp(~0.159*t); t time(coun ) = t; end plot(time,u,time,env,':') hold on; legend('Response‘,'Exp. Envelope‘) xlabel('Time (sec)') ylabel('Response (in)') ' Lam Mma bﬁm “fig; (8% ®E2t\$\$é3§3 {6% #23ngng a 35%“ {£4 tgkéada 2% “*2 agghéggy? tgiwé {9% M ﬁnk???- <f=/w§i=2”§ 4,495. (3 ; L ‘95 M3 «L:165.3 a' 1.45%” 164 165 166 167 168 169 ...
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## This note was uploaded on 05/09/2008 for the course CIVIL ENGI CE 511 taught by Professor Lynch during the Spring '06 term at Michigan State University.

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Homework3Solution - Problem 2.6 1. Determine deformation...

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