review_of_diff_eq._soln_of_second_order_2_28_05

review_of_diff_eq._soln_of_second_order_2_28_05 -...

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Unformatted text preview: Measurement and Instrumentation 20-MECH-370 Review of Differential Equations: The solution to a Second Order Differential Equation Representing a Spring-Mass System ' Note that F(t) is the input to the forced system and x(t) is the output in this example. Mark Schulz Feb 28, 2005 31‘): a A n Km SJLL'Wty {,9an +969; = m 52' FZ}0‘KX“C>& : PM? «+6»? +~KX ,: FM) /////I?}( SCVHM UL A, z W£3245675+¢2>f } ‘ £14m: ‘wk —~ rm: ka : C /6m 60 +42€d ) (ms) 69:: ;9§%_\ driha j ‘ 5019*OjrnGJ L . ‘“ Mk I ~ «we. [@ILOQCOSWAJN‘gz'Qraz)mka = {>ch m\% alwo mkwn; OWL 332,ch Qaiuflflvm'n. 0W: 03:5 C?:;”O/+§§, (9mm) =~ 02/ @4ng mm w :7 ‘m x J I mm: C [mum +~'(asmw wig “6% § MM 0 ' Nam/14 X5?! moflm WA' @ 4 p‘ " Reine =04 ( mag) \i‘ Acme :fi, / . ~vat v , , $1339; : f: [Aarwecgsuwi 7+ fiwggsmwdkfij N g; *y A 636% do; +‘Acose anarcxv?) :r flém 9) W) = A6, , art/(9)375 +6) V cum 6 464 £172,903an 2‘" > Ngfifiw fiwi 'Q'GMG » {7“ (SVIéifi M-E 33) 23M Sam‘w‘n KFGU m32+<>z+¢<><= Ht} (243) W ‘4 E; C9$ WWW. gacgy‘) @ J an 9". A ' » [fix % C \Q +46%: 3 E: cflhfilrf ER»:ng {cam r: /M c Q f. 2 70 X+QZWK+WMflm§WW&i Gw} @ Atom a glfiw XFH/zfla caIKNQrf—fljéz (Jo/J /5 759 X/flz’rfl; Cos mm" + 355”?er (22 f m A0: M! g:— 757%.) , m 3' ‘éx/Jrfi; Smer +w‘7rgxcus _‘ (223) J 3 'WJ: Mswm +@s smer (2&4) swam x?! if, 2; m w My As +93:er §5+VJ?A§ 43; W74 + wmfrgs - 12?ng Rs +9665) 5m mi : o I. 9* i (a; (W5 wifllcs mazwwes : 35> " ' a)“ / WK fllgwwkws ‘3' (NE W?) f5”; 2 M ‘ .1; .\ A5(g5 ‘17) ~ A5] 6; i'r’HZa Ao/ Q/ ’ Z (M‘IWJrEjZfCDEI/JWFBZJ z Q/r ' 23 WWY‘ L N1'W3Z‘) @ M we} : ,40 awrwa . , , (a G um Tym‘nfi fid‘ i: K565 NFM = Avfi smwhag Ac, (adv:in \u \cm H, 6) Mafia 1.6+“ . . _ W6}: A ewe "EURO Losg’ 7 :74:(X6°)f’4°c055’y/5m® : km =+7§w~wémtmém +a) + n53ng Cosder/E +9) "fwfir Pb SMMrvkéqs) ' f = “£3.39 V9729 +‘A UMCUSQ "I" 0&1er smzf _ H >2[® *3 (‘fiN’SmQRAJA C@C%)(XI(Q)QQQ(0$§5) +* (/flrfiwmg ‘ grizQ e: 55 [ Maw-mm ] {N ‘Wo‘r 336mng + ‘gW(><ce>—~flocos¢) ‘ 3‘ s _ J H :17}; w ‘ ; Jim r, ‘yvm *x ifi‘w, JQ pfiOW fl . ("5 39>); EXAM? E STE/5W? $01. MT! {N ——————-————————1 7‘: ,, mflv‘wé [(W’Wdr)1+(21 W49 2] Z k»: 2 V! Q‘QWW‘Jr as 4% _._._._.. MW 07,4 OAT-L“ M” P? m W193 W‘ A “3 y} C 641% /v% 043 M 1‘: PW 9“} t: I x Z. 1 ’A E) )€° [GA + 62$” j 1;“; g6) -( m... (é: “(I‘lfium 3 E: r: We)? WV 2‘: fifiév‘a’vv _ V ' w *if j 1 :2 3:) F5/[( I u V:- V /‘ e f r I in I. I, 33’22 a w ,9 a / j" J I/Zffldfi w) ,1 ‘5’“, a "‘1‘- ? A, Q fa f flask; A MR$ DJ (Lhmm H Prov” Elna“; sun/v35 @ ...
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This note was uploaded on 10/13/2010 for the course MECH 370 taught by Professor Markschulz during the Winter '08 term at University of Cincinnati.

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