OMU324 H.W 3 Solutions - OMU 324 Sysmm Dynamics &...

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Unformatted text preview: OMU 324 Sysmm Dynamics & Confirm Homework #3 Sahatiens HACETTEPE UNIVERSITY Mechanical Engineering Department OMU 324 System Dynamics & Control W Due Date: I) Linearize the non-linear system given below by using state space method. II 2 y+sin(y) + y + y = cos(u) 2) Mass—spring— damper system given below consists of two masses “Mm”, one linear spring with a stiffness of “k1”, one damper with a damping coefficient of “c” and one non—linear spring which is defined fk 2 k2 (X2 *‘ x1)3 . The table will be useful to solve the problem. Parameters Value x1(t), x2(t) output 10 N/m 1 N/m3 i0 kg 1 kg 1 Ns/m a) Show that the equations of motion are; m322 =f(t)—k2(x2-x1)3 M x! = 1:2 (x2 '— xl )3 — c xl — 1erl , where u= fgtl is the input force and x1&x2 are the positions. b) Linearize the system about umO. c) Simulate the linearized system and non—linearized system for: M l. A sinusoidal input of small amplitude 1959?”) Z“ 9"; x i: t a f “w Jr“ 3 2. A sinusoidal input of large amplitude y g, 7 taxi?” (W gr) 3. Comment on your observations in part (a) and part (b). ‘21“ Homework fi 3 @ Lénwizifig “he. hen—hnmr $75M gWQfi Osa’v—g Single. - ,3 Law}; ‘0 29.3% E] +8Em€§>+gfi%a: mgfigj , «Lima? 45kg, 35%;,WM M (gioia §?aw- garm.) WOQW‘ Kiwé/ K213 / K3: ‘j‘i: K1 K2: x3} = ~ezm(K3)«.-><; mafimsw (éfifiargfizw “‘4 5- ” fl (Equi’iéim'ma) uzuglafifiiagm‘QJ/Q) h W :63 a 4L. K{~O 45‘ K9. K3 =_5:nLo)wLajtwKt+msu- ilzon‘fl AEZQ “ O 0="O'-O—~?K{“§~.L xi :1»! XlLQ, K35: O .flIl/Qrejore ; ‘9 4 R = o o Qi-efgsgfis-Qma g ) 534%, 6M gx?’ Egg “1. —Q%L—caaéx?3) fl @1 Egg. gag QM. émxg 3 ° M wk” 0 "’ K :K .- f“? J a guy ‘ 1 O fags) KQXKS ""- 1 (“g E/abé “SWIU “Pg ‘3‘“; if: W$ifi€g§§)m%a wfigéfwg 6&6 (Evofiucrge O Q 3 3.: O §< .4 K1=O;K3;Q 64 CE© ( Limmci Engtl’fi'Q-a Q >Z=1QK~+IEUM bail: ‘“ O c; Q g 4 0 vi ‘T ? g {g . '.M-' 2*sz m E {M w 41% {3 I. I I“,W-&5MWWW am “WM unfit” as? 1% gag-@ré a? sgsiw‘ j-‘Ermdlggg {gag gaggiw Q:_€('{): Q . f f m (D r . efime; ‘21-: Xi! @ ft; %2_:'>fi,g_ 8% %a:: ?$2., _%%$?;g~ Fro“ 941.69 3 @ o in ad {an r. 0 1 Z, 11' 0 Q?” 0 2:1? @C—SOCQLimg) ~ — {Ail 3%.. & as. fie. 4” f. 1.1“ _ a1) '84:: 3h. 9%; §%% 4‘) #dé;;&i[iau}fl_m- 1: --—~= g: a}; gsz gig-a... 1 , M 8% 3 Ms, “3%; 43%;? f3£§fi=££fi 3 8:32 g8; 4&4, a é%: fiQz «gig fig; £h$ 3,!) _~ P % m m éée'ésq E <2”): ,0 W3“p’ :10 g I :0 r_°_?.__J_..:-i: ---—---» «a f & c3211 3&2, :53 %€’? I ‘1' ’5 EL -53.,R‘2, . 89L- :7 1;: LEEIL‘; ’é%§%g+f§%§%i “3'31 3’34-55 M a a M a igi}_["%%g+(éig%i>‘3%fvg "3% // Qatt‘ “M 34):. a -C— 3.22;” M '2. ELP’L. I L£[3%;—6Z5%143%i] // 317:3) M £14): : O g%ki .5; Q1. M @ LEVMQ. Som‘ofms a; §%u€§g§w~wem) O 1 C} 53 fat-“PET?” :. Jc/M’ fiCgM O O 3% o O ’0 i 'i_5_‘”"bmhuw~5wmwwwfég “SE 3 J“? “Md-E 1% uneK?ec.‘(e,ci i F0; bwiifié’iflfl} fiwe msé—wjy $2.. 9U Efixzaé’a {as 4K9. raw {3 Where are, H“; sgglw cw wo“{ La iiflmibfl‘uid LN, 5’14 “3,? a“,ng mWWMWWW"‘C:)F—--é~www«wwm~———W ° ® jg we édnsi‘cier éitg; gqglvw Lg \mrhcgfi w; .944 gamma—L.me 513mg; :53 39:3:{12‘230 6; mi}? 3 3(4) " Ez(%3-%zf+m-5 ® Tm kt'gn g fit :3? %f “3:2. 5 '3 ‘ $2,353? 132,42 Egfifiérqi)+w3 “EARL! 393%; M M 1M R: m 34% «siziwa __H_~ _..ELA«_.H --fi_ “WWW 3% 52.3% «3 "‘LV ‘- 522;; m a ’> H” 3:92. :3 3.53% .5 £2. 3% -1 Z 3%; M I «3&3 “r7 3 ’)// Ma 3 On 3%:? ggg 3%2, 3%}; g‘géf 8—“ _+31c1(=a gf gigs—“Q __ m— g g . g 35;”: M // j / (EX-PL? _— ~3éa, (vi; $32}. it L" -“= O I” &%g M ' ‘1 3% J Eh?)ng ‘(éwggg wines Maia jfiaafigim waxy” O ' A. Q 34: ; w“7%(=e=g-23~a .25; 3%: @3402“ M M = 3% M M O o 0 31:2 (g3-}i)1‘ O bfiésivEyEi)!‘ rm Oboe I Simh o m, g $4.9M; EQWSa 0.? .pérfi'!’ Sup-PW can (9" he“ fimtgéj We m W giié-‘E'W‘ {)4th we {think Gfifikw CS we; @QLA samut‘im Liam/( Jackw ® R 91"“90 “5Q “W4 05% mm mflgg ® a: fiE‘WSDfLG’WW“ 43—? ‘9‘3 Wéfiiéuéa; .utk) 4L4) g Q.QL§.‘,1L+) u, Lu!) :4? C4 )= @933“ )= , Gk “3"MW Q‘ffiiw E we'ia'aag‘fi; >2; +L2LLM-N)'3_,£§>«5 —.-. 0 G) M gm .5. iak/b X + «unis.$ «gnaw “m k {f} _ ‘ I Simm‘lh“ “3? “WWW wéeaq 3": oluLmaaA. («a u3i% flaw/{Abba Wm KL 2: Xi- : %.?§; *1'%?% £1——CJQL+J_‘7)?9%$ :9 :t v {Bani-g: 13 1:: 4241*: X“; 2‘1 zig-QLEBEL~13.?h3£3+#.£(.+). a; RLAZRRSKL~*§.?Q,SRE+%§M(~§L WW-»p—.-Ww~mm m. ‘ e H. 3.59. M?” 4/ 5A3 _. W 3m; gem-hem; w? gmm Mgmwle, s_ E 33%,} : i {303% L0.§{)w§ .Ewgaa gyfidthQQ f! I ...
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This note was uploaded on 04/01/2012 for the course MECHANICAL MMU-324 taught by Professor Çağlarbaşlamışlı during the Spring '12 term at Hacettepe Üniversitesi.

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OMU324 H.W 3 Solutions - OMU 324 Sysmm Dynamics &amp;amp;...

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