ps5_sol - M 56 (5"! Lf W.-wwl/L kk ‘3 an“ {MAS...

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Unformatted text preview: M 56 (5"! Lf W.-wwl/L kk ‘3 an“ {MAS For Sin/\fJUf‘iHJ N & P-EQILP A M JJVX’! vu?"€ :A Walk 05:- ilk-e {-‘mcim, r1 WW5» In T max mule! Wage g“:k~.ad 53mg ower" 519%». "The- ‘3‘)rmj‘por4'1‘ns are ~ A); .—_ OJOG, E,, : lacs 5%, an: we (3%, qt: 0.31.} (3,1: $356253 71KB f‘b'H—x éL—C'gd Maév-EA («ALF "Fy'£>~‘({{?.Wv can "?nl}g_ '2. Q?f>tl9g Una-1 5 rem 5- - m ' - L ' “(93 " 57M“ _ —_5 ,3 and mmeu 8‘3 6m,“ T '---F ‘5- Mlle.- Gfiw. D 26’”‘ AM 0 r“ = '_L 5‘“\ U5 enm :' O \‘l‘el " ‘V‘g M-Elfl‘m‘lq{d ) (“Ohio-«3 J - ’ 90: " W5? Wfiflnu q 0°. iii fifirflkk, 'Ibfikoz 1) {Mg-ix “A "(’— ?o€€ 39% ‘Qb-fl r M} aan) \1‘ rm cA‘m‘ 5. 44w 5 m m Ans,- em», '2‘ 0 tan 9:5 v’ 49x33 3 W0 5"; 3 La 3-15 *, J,’ EMF; TU yawn wows ‘\._,_mw_ri _ .fl. ww gum-4mg «NM.._.._, . . .., --4--t'-"b LN"— X ‘ . _. . If, ........ «pun-mu- m . _ k .u- mummw—WflmeKWReuun1mmum-nw swam“-.. mwmw%_ Mu» 5% y M w y ._ m MoMaCaéLTwaqfo-m m4 3514:“); “Hank” 3&4“ Ennufl oa/OO/Oo/OQ PméU-CPC 1’3. CLK"\F“‘"&‘EH 72*" — “Mae ~15” w WK IQ snakkaqL “2.5;; (“waiuwem m1" \ a 1w»- 4.4”» MUN/uth MK 2 ram: M-M. K - A .‘ 71x9. Cur'\:-"“!'-/£ '-’- —O.'3‘\0 W LAM Awe} 4M Wf‘weflw f\ M): = ‘*="-‘*“ N__‘.__M . WW9. 4mm, ova-‘5‘ um’nc. rewind-£1 aapfs JEW- WW5; {(Lquq“) ($9.; F7, (mg, 4mg.) / 3; WOLQV' *o Lam”. ma SW9 Lrfimiml —beud~,ui~r- Fuu‘fildflsif NHL mm? km. a 31muuLK‘v-I't towup, 5a 4A9}: .2 may [31 =.!Cojl A‘Sa/ U34 wugfi. “41‘le anL. (Ly: £01 .{ifikflu7. 1.6.v04'crffi’ l . {wwfi’s «mm as O/Qo‘llvnolo" W9” “1”” 'g‘”‘-‘l""i>€‘~’; MGM“ .-{£\.fi~j Ix_,‘1,\\ when/“seam I'fiflnrmidhfm SrHl-Cr’f'r‘h'gs bf-tweggfi Mx an}; H V‘AWQ WM $.eM-0-eb« ij AM A H. MSE b‘t‘vi Hull: gamut; 13mg 2 MSE 644 Handout: MathCad Session on Matrices A, B, anu‘D E} " 200 E21: 11.] GIZ 1 8.35 N12 ‘ 032 (units are GPa) Define the Compliance matrix [She Define the rotation matrix [T] as a function of angle‘ and detine the inverse '— 1 *N12 0 — q 2 — -’ -' V a“ -' r' - "J ‘ w". ‘ t.. E E] E] .‘cosiat, sunta, -Los_a_ sine, LN]; 1 O Tia) i sin [3:12 003332 2 cnsi'a: simui q 7 WW 7 . . . t E1 E2 1 L cosia; sin-la) sin-1e; crasfai cosfatz 7 sin ‘ ailz 7 O 1 ’ (312 I I O 0 ! Tjnvixaj ‘ Tie R I (i i Detine the stifiness matrix [Q]12 0 O 2 Q = s ' Define the Compiiance and Stitfness matrices atter rotation by angle a (in radians) Snmrai 1— R‘Tinvtai‘R l‘S-Tfa] Qnmljti '= Tinviaj‘Q‘RrTiaj-R I Detine the Compitance and Stittness matrices after rotation by angie e (In degrees) ." n i i TL ‘1 r '. -- ‘ . Summer. 1— Snm 9‘ | Qnmd“~B' Qnmie 130; ' ' t, 180; ‘- ' N l A:h,1heta.N,12: E [‘hk_l hkijnindititctak} k: D N -- l B::h,thcla,N_: ii 0.5- 2 Mth If -- ihkf)‘ -Qnmd.;thctnk;; k: (i N 1 D’hth N“"] \""h ‘3 -- d-‘h'* , eta, i.— 3- L I; k?“ Qnm Item-1k". k= 0 PARTS (a and b): Define the h and theta matrices i i _ 2 ‘ 1 th " ’l ' ' U itipartia I 0 -im' 2 Chi—[m —‘1 7 u i _t) _ 2 A_purt_21 : Aihfi 2min, thctaipaILiu. 4': B_ art_:1 ‘ B ih_ EII‘Ln, thciuiparLa. 4; P , P P D_parl_u 4 D i'hApartia, thctaipm'l.,:-1. 4) w.“ 10’“ ' ' .: GN. I .‘ bmomemhpdn—d 0 ‘ mm 1- '2 B_part_u-A_p21rtin lABipeuLa D_pu1’l__:1 0 J 937-10 4 k_parl_u 1 F I'bmo11*1er1t_part_e kiparlia = 71.10_4 Um U ZQL] MSny (AWL! “(W ‘3- SO‘UJ-‘dmfl 5 Ta?“ 3’ P” (CM/$.13 m. £994» @3qu m. Agar ‘e {If'lwr‘w‘ crr' “*6” M a. 3w«m-&.+Yi'€: st. {IA-a M5192. (ad 1 5 l A‘LQ‘NVD‘ar helm“; gm...” Han-i- ' I 3.; HS": M" —r:rs°/+§°/4§‘/-~.+g'° W T‘ A 4gb/_%o{_%o[qra uo‘m+ reqwng, is PART (0): Define the h and theta matrices ,_ 2 , i 45 2 l 45 hipurtAc 0 -ll) m thclaipartfic - I g 45 ‘ ' 45 2 , , A_parl_c i-— A [h_par£_c, thetaipartic, 4) Bipartic B f'h_part_c, lheuLpurLc , 41 D_pu.rl_c i - D {h_pa1't_c . thetawpartic, 4) 10 6 1 t : *6 GN. _ hmomm ‘pafl—c '0 mfm F -B,parLc-Aipmlic 1'B_pa11_c — D_part,c 0 _ ‘ 3 1 3.] 1 ' 10 kipurtjc - F l>bm0menr_part_c um k—P‘dl'l C = 3.11-10 3‘ 43210"1 3 ‘ Mezaé 0"‘4‘+ WM H‘W L: Scab“ S, Tang 5,; ngzm‘ws “FREQ. 5‘15-‘(L-M5J5 ‘ ¢?¢‘.’ A [turbo— O‘ 1: 332m: .w/a arm“ = gfioom‘fi: EGFWL1 c 2.[- (mo Wag, W :Wt’mw 39g; (5.17; =5 é""r'""€ -= 58 r0445 $3 im'?’ é'wmwv: 7| "3-3 A. A Mai-e é Win?! (3X9. df'nvpc‘ W" G/EI I: ’3 char Jun-£- E292“ Fau— $2" rec-3m! sw [an 33-1.”: Qwrar$ml Aérqfiekwj an on; JoTegarkJ,‘ 3?. FmaST'eLe.r ‘ba‘rk CDA-La Jwehauu‘ fgkm‘de AEF>0"/ w-e UM. 43w firm/fey A); r-s'ml'!“ ELM 3' r’QC.H;rfi_ Asks. Cane c', -F -: "ZINE: .> Q“: 93 43'"; L MW: EA: ~ '4' A?“ E». 2' (J a.“ r k E! 1* 61:51?» 0 (,5' \ 0'3! "M0679, (17-05593, W, a; Kimmy (- msu- u? Hue! Laws. "—3.; e A N _L <EM—‘f‘3H3 E{{=/\E'_£+M;EM:Z+? WEN o in; l K \r 130% W “W x’é ‘MS'é’; “H was SQUMS fonts). 52" ‘4'. N42. use. HM. Tug-'- ucM Cx'.\—-e,arcum failw-Qr a; : unmoqu (3‘ 7’. Sufi-L7. + 6‘12, L {512. L AW , d C; AL 7—- + 1'" 2‘“ FM" SOME { 5" 5'1 \ GIL A. “CPL : SQMVE l I'M. 153mg, s; 4:: GLQMVMMQ 4&9 Voiuec. CA3 57" 521/ (372 i vi€w"M: o£ 4th. owhecé Eves: 55m ) 0V1“ Syx=fim ' u do Mafs/ we. mil—z N” 2' "'2.— W "I 5” r; )fikl 5'!“ +mV-\Lj\(3; + \j‘sL‘ (TX J '1 ELL :2 4,. XIK’ch‘iU + 4— l /./'/1rl.:mm= 5:1 —— *l*25§<K+K.jq,flj +3117f€593¢ w - GT we; ask £04» 43% Lug“ Wm? 54‘ 1-. FGQQ- K1,: - sake» g5 ‘31 = 3M9 \qu :7 core 6‘” :: Caste (Sm + 3&6»:ng 01,3 511’ = SIX/{Le W Est-#63 Pow 513, a —s.c-.ac,csamw +(mffl91'9‘ 54A 3'5 5!} SMCE (57:41-17 O-Sfikfil we 6'” -: <57“ (cute-4- 56‘s) €0.9e}\ : {(9) 5"” cpl-L :- 5x54: h (0335 K $ ya 1 m (-smezose + (mie'sm‘w = M6) 61w L _ (-‘C Lu-{i FLUK— 4911‘5 :Q-In TSE‘Q’M‘VH (VY‘q‘QV‘g’W/ MSéh‘f‘f— PM 6‘ Ga MathCad program for HW5, Probiem 4: fit; = {cos-ft]:2 sin-1ft) -cos it} gftj: : sinfr}2 sin:;L_I-c-osx\t': ' 1.. h;_t: — smktpcosfi‘; I 0.5.Kmsxth ' Dowsing; \ /1.\ \., ,“...‘2 F l. ['11:] fall-gm- I‘g'tq ‘ NHL"- m ~ 7 W "W ‘ I !—; 11500; 15002 .‘ 50 , ,‘ 80 3 I ." 7|: ‘1' l Rim; 2 Ha I at - *- 80 9 «5‘ Hi .7 d‘: org”), = 210.633 “We ofla; 01:30; = 227.337 " m‘ a \_ tr 01.60; _ 93.991 0 ‘ I Iii? 0 15 30 45 60 75 90 . 2| 5, W4 m4. 9(-"’"3} E” ; E4 " UM Em / _ =v IVAN“ (-Qwr Law“ \ = I = ;— mu (ME) Eu : flE;+/\F“QF§M — / 0H4 flow; olflrlfi mag ...
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