Midterm_2_solutions

# Midterm_2_solutions - _ ME 670 Midterm 2 12 April 2007...

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Unformatted text preview: _ ME 670 Midterm 2 12 April 2007 .mmmmmmm Problem 1 32 pts Problem 2 35 pts Problem 3 33 pts Total 100 pts Name Problem 1. Answer the following questions for the given electromechanical system, ea) Write the governing equations of the system. Do not combine equations. it >. {W’s - gigj-g/ﬁ’e (millet; a» a F” 8 i%~wg F t Silt 3i (5. b) For ei and TL as constant inputs, ﬁnd the steady state output 030 if I; is negligible (J; = 0.0). Ea ww’éwleié ml” 5.1, (‘3... :1 .w _ k K/#®&ME<QW» C) A.»€A:«W§v \ Wm 9 k Ix — w (9‘ a “7 * % Elk)“ 4,95 inu'w Q Ma: w + mg, I” l? w- ay ‘1 “- I F: " E 9 (.2) fa B ‘ ﬂ a BwﬁwﬂsmiJ‘l tea wtewouésri k 2,. F T :0 Fr “€731: “gs; rttﬁsfiitﬁ “L r L- - ‘21 e m r “2? 34%, K .911fo v i'" - l R We “ y; es "“ M; ii T «3: Kg: @1ch 4. c) Leth = 0.0 and put the equations invector-matrix form with coo asthe ou ut, and TL and eiasthe inputs. Q "M W“ f—‘x . gnu ﬁzwwkmd I; i ‘3’ .. '3‘ - Ea <3 E r); N“ i 5*; «3 aisunjg‘mkawpt WW 4 e 3? C74 m “ r t \$14)» Kg; 3 i3 ” "g" mg” ’Wi O ‘ Q '* g/wwfwoigiwl éwii LC”) 4‘ .37 “hi €5.33 4*» t “x g“ ,_. m! magi“: W “T g m Eggm’ E éé‘ﬂahig TL .1?“ 9 —*——~ ‘3 s! in géi p (as? g :1: a a? gas“, : away 3 La.“ k i (1) Given the following simpliﬁed A matrix of the above system, ﬁnd the characteristic equation |sI-A| and discuss the -3 —l m 2 ~£ % MIN/m ME A; {24 / V m a: t ‘ :5 r ” M, v '1' :"w M *3 x! »‘ n a N - 3 3%,? i JV 5" t“ t L 35: JR importance of the roots (eigenvalues) of this equation. A=[—2 l J 1‘ “3:” g * m Wang a W (a; t (Z (5%: aw; gf‘ we r at/ft’wﬂ? M as: {aiiﬁ ﬂuff/779%“; “Z 6) Based on part d), sket the expected form f response (00\$; for a step input of ei(t). Assume TL = 0.0. You do not have to solve the equations, just sketch the form. ' y?” {We 9 i Probiem 2. Answer the foiiowing questions regarding the given system transfer function: 90m = gig—+1 Q10") S (723+1) ; g 3.) Write the ditferential equation of the system. L 'm. ' t ‘ A4 :ggma gngpi/Jg we Qua/~33: } 4.2220 w"; end a phase shiﬂ. . .. ¥ { ( ) Mai-me I i “é 11. / MWMWV w E :2: JTCQW”: / sJ [I] ” 'éﬁw’g: LAD WAN,” ,thmrwm a, p ggwwnz‘awrmdasuhgwmg W. Jﬁﬁgﬁw WWW f: L, i t o 4 ~ ” , .... ‘w w,mele ' Ln A 1.x 1. L”) i kw f‘ 5 WWWWWMWMWWWWW“ 3:? ( ‘ ‘2‘ r v [M ! g Q 73: gAééQﬂ/‘orca‘gifemk +32%; or m {55,0 9 “3420 e d) Use your Bode plot to ﬁnd the steady state output for q;(t) = 5sin(100t). A» 2 “QOCQL 49%” «‘7’ wf’éyaa (0511069 Problem 3. Hot liquid is added to the pan (shown below) and the temperature of the pan and ﬂuid comes to a uniform temperature Ti (t) very quickly (at time t = 0.0). The handle of the pan will start to “heat up” from time t = 0.0. The handle has a width w and a thickness t, and is surrounded by ambient air at temperature Ta . Do the following: a) Make a 2 lump thermal model of the handle ignoring radiation and labeling resistances as Ri’s (i=1,2...) and capacitances as Ci’s (i=1,2). M ’ ' “ ‘ Tarn {as b) Write the governing equations for the two lump model (keep using R’s and C’s). & nip 73-x“ Tctz ‘ C 2?} {gt-9W? \$11 4!; RS 7 R1 E1+RF m a Z 2” '3 -— ~T7‘eTa" :3, Q if: WW? R|+Rl R2 Rig: 2» M I K c) Deﬁne the R’s and Cs in your equations based on h (h.t. coef. ﬁom handle to air), p, {a and dimensions of the handle. L/ i g E I R .1; W : m e s kiwi; >. Mitzi»sz K2 am Cf Pan!th _ E a 2“ ii 5 _ LEE 3: .n i C - ,6. 3 ‘9—«3 'ﬂ :1 w ‘ i m/ (54% M [ii Mcﬂ 2. F L cf E We? ...
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## This note was uploaded on 04/17/2008 for the course ME 670 taught by Professor Fussel during the Spring '08 term at New Hampshire.

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Midterm_2_solutions - _ ME 670 Midterm 2 12 April 2007...

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