{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

OMU324 H.W 3 Solutions

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

This preview shows pages 1–13. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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% [email protected]é 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 ...
View Full Document

• Spring '12
• ÇağlarBaşlamışlı
• Kilogram, Mechanical Engineering Department, Ankara, sinusoidal input, state space method, gag QM. émxg

{[ snackBarMessage ]}