ExamIISolutionSP07

# ExamIISolutionSP07 - ME 375 EXAM#2 Thursday Division Shaver...

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Unformatted text preview: ME 375 EXAM #2 Thursday, April 12, 2007 Division Shaver 11:30 / Meckl 2:30 (circle one) Name 50 Z M‘HOW Instructions (1) This is a closed book examination, but you are allowed two 8.5x11 crib sheets. (2) You have one hour to work all three problems on the exam. (3) Use the solution procedure we have discussed: what are you given, what are you asked to ﬁnd, what are your assumptions, what is your solution, does your solution make sense. You must show all of your work to receive any credit. (4) You must write neatly and should use a logical format to solve the problems. You are encouraged to really “think” about the problems before you start to solve them. Please write your name in the top right-hand corner of each page. (5) A table of Laplace transform pairs and properties of Laplace transforms is attached at the end of this exam set. Problem No. 1 (40%) Problem No. 2 (30%) Problem No. 3 (30%) TOTAL (***/100%) Name April 12, 2007 (40%) PROBLEM I bode magnitude plot for the following transfer ﬁmct Be sure to clearly label all break frequencies and slopes. 1011. tron 1ma (a) Draw the straight-line approx 400(s +0.1) U(s) (s+1)(s2 +0.4s+4) G0) Bock; Pld.’ Mwitude mmmm s . , ._ . . ...-.. .45--.-- ....T..11.J -....J-l-.---1 ....... ---_--.....---,_--.J. ........ 1......1 ......... - ..... J ........ ,_ ii, I IIIIIIIIIIIIIIIIIIIIIII 511.3nvirll .n w .4; tunic-11.1 IIIII Inn » . u I." 1 4| . . _ . . . ..--...4...:.!.._.-....-- ..... « . ..-1-------. . . . . . -..--...1..--.-.... ............. ‘ . ....... s ....... J . . . . . . . . . . ........ ... :1-..-..---..-.....--..------- . _ _ _ . . _. . . _ . . ..... ..-.-.{Tl-1-..?--.--+.-.--. .. . . . . .. . . . . . . . . u ‘ . . l . 1 . . f . ........ .:.......:,..,....-..._..,..-....l..,.-:. 0 ..... .-------..-.--..-..------l--..---- 1 ....... “.-.---u-_-v;..-uv-unlnaonua: Alta-Ill-- . g , . . _ f , . ....... ..---v.9-tu.-32A-1:1»-lI-I-xv-w-o-tt-Iu . . . . . . . , . . ....... ..-u-r-vwrrtt-rn-va-n:I: nit-uo-ult-I-v . __ . .l . . r.....-f.--.--- . . .. . . . . .. . n u H o n..- O . ...--- ----- -l ---- ---.-.-. .1»-.. 1 -.- -------- w-l.--_- - ----- .(Ll-i-l-Ta-r-l. . ...- ..r---o-il-l-I-- -o--.:...o»¢-‘:3.251111} - . . , . _ a -...-Ill-:4I-1-urll11-11II-a uu-u-IIA-VI-Ir- . . -..--All!J-annI-I-arwwr-u-ur-‘ul--tr . . - _ -r- -c.r--,-I-pIr--rAIb-a--Ir-.-II--a- - --13.3»:..L19!-*+a_nI-wnlhrt_xprt-x n p , --..v.u-,-....n--r ill-«01:71.7. . . . .-..--.. -._- ..... _. ....... -..T-.35.1.....c2., ----- -...¥--.--.r-.-.... -- lr-IJ-kJ-d-n-l- a. l r 9 I I ~ . — , nu - -,n- A. - ---“.--..- ..U.-.u---,-:-n--AJu-I.-.,1 -.alaa-Wo-q-i-vﬁti-i. -. . -7.--.r----h...- ..... . _ . ,_, . P, , . strut-«alarmnvrwox-v..- ....... - 3443.11? ., h . . ------- l1 . ,.., u . . ~ ------- nv , . ----.. 4-2.)...71v1-wtv 1...--- {ll-k ., _ ,-»-!.n l... :1- ---------- .- . .y [-4.0 “guilt-v.- . -.--...+:--:L.--- ...... n, \ .----:..-. ..... ,. , t ~ .-_ ,, ,u a . . . ...---.. -.-.:....:.-.: ....... -1.-..:,.1:--.. :35..- ...... , F . _ , . a . A . . a m. LIIL W W muéBE 4-0 (36.! +1) —. — 6(5) + 0‘4-3‘1" 4') (3+!)(SL April 12, 2007 3 Name (b) Determine expressions for the frequency response magnitude and phase of this transfer function. 69;») —.: 4—00 (iw+0./> (\Sw + l)((4—‘w‘) 1- OffJ‘u) /6‘(J‘o)l= 40° Q‘+o.l‘ (c) If the input u(t) is given by u(t) =85in(t) , determine an expression for the output y(t) at steady-state. 39.4-6’ 48 3 cf? A i It \0 w \0 u April 12, 2007 4 Name PROBLEM 2: (30%) A galvanometer works very much like a dc motor. It produces an angular deﬂection that depends on the current passing through a coil. Like a dc motor, its torque is proportional to current, i.e., re = a i , and the back emf is related to the angular velocity, i.e., em = a 6i , where 0: represents the torque and/or back emf constant. The only real difference between a galvanometer and a dc motor is that the motor shaft is attached to a spring. Assume that the inductance L is zero. (a) Write down all the equations that relate the variables. €50?) —» F55 + am April 12, 2007 5 Name (b) Develop a block diagram that clearly shows the electrical and mechanical subsystems, as well as the electromechanical coupling terms, with voltage e,- as input and angular position 9 as output. (c) Using this block diagram, determine the transfer function between the voltage input e,- and the angular position output 6. 34* Gum“ Item‘mi «Fem—ALMA Coop wHk ( "‘ 0(5 6‘0) = 7%“ m / [49) _. f__<_ _____..__.__. S 5‘) R Ts‘+6:+l< : 0< 06\$ 5“) /+ 2,” 54mm oé 7— April 12, 2007 6 Name PROBLEM 3: (30%) Given: the following hydraulic system: Find: the transfer function between the input W1 and the output W2, by: (a) Writing down all the relevant equations (20%) w (b) Combining and re—arranging to arrive at the transfer function (10%) (a) We. = EL!— §(—W|1)M C( Q‘ C! Dbl; + M; = — etc, Q). g <R(C(S +I)U’z(s) 2 'ﬁQék/zc‘) ‘ % RLCL WL = Wt + (IL/I2.— WL ilk/(1(4): - RaCIS‘A’aQ) {QC‘ y+ I C (ﬂaw/MW wxs>+wats> = wits) ~ W ﬂ(ClS+/ (RIC, git/Xmas“) WLLr) +chtswzh) = (mg m) w, (s) ...
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