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soln mid term s 07

# soln mid term s 07 - Measurement and Instrumentation Lab...

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Unformatted text preview: Measurement and Instrumentation Lab 20-MECH-370, Spring 2007 Mid-"l‘erm Test Ma}: 7*, 2011)? Open bank and netes. ﬂpen eemputer en]? te access the course web site en blackboard. Work individually. Pic-ease Sign your name stating that you have dune this: examination nu yeur- nwn. [ have unl. given or received hglg on this exam: Student N umber: Selve all prehlems. SHOW ALL W'GRK. ‘Write neatly. Sec-d Luck. 1- [25 P153? An electric cireuit is shown homo». A steady-astute sinusoidal input Voltage is applieo' to the circuit. Uae symbols 1'11 the solution. {a} Derive the equations for the steady—state voltages across each eiernent. (h) Derive the equations for the magnitude anti phase angles of the steady—state voltages at each element. {e} Draw an approximate rotating vector diagram showing all Lht: voltages in the quadrants and direetions. UHFWL V‘ﬁgw 5H wake "i 5‘7“ I ragga. 5-5.3,» . g x \JR: IQ 4e? r: a:th :13:st ‘Ef. t g: .u d - I I '2" I q We ‘aginfdéﬁmﬂi -: “’9”! “3 \ ... W Va *~ cat-+- (ao‘ tahﬁtfj <3 m {WW Naiiﬁitlﬁzﬁ 2 IQQ, It“ 2. [25 pts} An electrical circuit model eI' a l~diniensienal piezoelectric element used in an acceleremeter is shown below. Derive the differential equation for the output voltage 195.1?) in terms of the current I produced clue te strain efthe piezeelectric crystal. Remember that I—‘tt'Qer. 1:..- Eli” e5 "f: J :‘H 312'“ :3- 1. ‘w’ 1.; + "d. .m... . .. ._. I If I' *1; :34; E?“ 3. (25 pts] Give short answers to the follottrin‘r-jr questions. 3.1 [5 pts} It thennooouplo setup is shown below. IF the voltage measured is DJJCIIE Itolt, what is the approximate hot temperature in deg C? The Seeheelt coefﬁcient is (1.95 111VtﬂC. Show your calculation. ‘ t, .. .4. (T. “"11. V’. tit-WM! :nettse: i n g Enochon Fill ‘1‘ voltage cl moi;- t MEI. jlmotion ' CI {Ter 0C; C, Ti ‘3: are 3C, 3.2 {5 pts) Referring the to the Cll‘tl'ttll below. explain beset": on the characteristics ot‘s capacitor, when will he the ~t'olne ot'Vo at low frequeimj,t and at hi gh frequency. . . m. - ._ “w. . 1. .... Tu. 1“ MAT? L23. Elli v-tgmhrfz '1'- ﬁt- If it} -_.-:.- “L! I; . R I '. I: “In {gill-1| \Idhrlmﬁﬂ‘ j t Iliad b PTZH-ILJ'J Q l ' Il5.- . l EC : 5......th ﬂ Wit. 3.3 {5 pts} Brieﬂy explain the working pt'inoiple ol' the linear potentiometer shown below. 3.4 {5 pts} Brieﬂy explain how the LVDT in the ﬁgure below operates. Also explain W111.-r the shape of the Rio waveform is difteront than the shape of the Vi waveform. 1:: pl emit-sheet Wiley: II-tll I I. I I r a - 1' F :1 E 1' 'Iull H? E {Lew tull’it} r 1 l I I- L ‘ |hr T” output wilege with 1:) hall, 1‘9 L the} {l- M-vl v v I'L- . I . .r. em}.- Jett of I'.-uJ.t i l l — ooze — + v“ outputvoltsgu with E tut; ﬁght of :Iull _ q ____‘_I‘_ W mugttetiu- t'ieltlt- _ and useotueted trolley]; wini'ilies 3.5 (5 p13} The equaliene and graph {of the magnitude eF the relative aeeeiemlium’ianLL aeeeleralien) that repreeent a eeeeud order system {sexing—mass system exeited by a base 1' nput) are belew. A particular system has attempng relic: M [13 and is exeited at a l'requeuey eflﬂﬂ reitsee, where the frequene}.r ratie is {133. Ueing the graph belew andfer the eerrespending equatletm, determine; (1') the ampliﬂeaiien efthe hese eeeelemtien ef the eyeiem, and (ii) Lhe rmluFel frequency eﬁhe shame. I J :- f“? -.-'._ {ugh . E £31,: Jr? ‘I ‘3'" f. V3 ‘ I} '5‘ l .u-F'-_' T:— e I § H .-=. g ,. ' - H e; . . ._ 0.; I} nag-4'! lr T“ L 2"? f r * h. "LL em _ it ',3 a? we] elliﬁﬁb L. em 0.1 1 ' V= 4%, we. acceleleulelm: . I .. 21. . _ I DE. —,,*::I ' —-.T,. I .Tl. — — —,.1‘, H; “u 11;] . — e nannin'r,_.":1‘:}rrre.-m'1'. Hi] = - '-,I';.Ir rr'n'hwpi'ugi'nﬁa' ; -= L “Jim: f:r;i.r.'.f rfa'sp-‘rn'wl'H-‘m. m: I] = all” MI] referr'w emper.’ ri‘x'spi'ui'nlmn'.' mi r} — -1:.5:il‘.-{-'-:-r- :31] . . .1|.-y I“: Huh" rrHJJrJe'fnrMmrm: — _ . U .- gum-,1. ' I. |_—|-—~ *4L|—:, ll'lll' _ “by, 1 _ . _ _ ..-._l_:a My: pun-s: mjgfe.‘ fp — Hall 1' '—. {:l ' . 1 -! — | * 'I."".I.,.- “111"!” “(FF-'FF’J'FI'IFGJL '2‘”: r] = —_'1:.I'1'1.3i[1[[‘IIH . _ Ill-1f: 1 J’Orrrne' Hﬁii-rj —' T; : 4:: " . 'n ':'- m ‘3' - ’ |[; |—;_|--l;-I—,+. ‘, -.:-J., Hm. ' . . . - 1 . -, 9H3)”:{r'npn'ac'emrm en'anpa'ﬂrrn'l" .'L, = '_I —._|Hgle:IJILL4-'J '1' I“); I .1 . .. . .. -. -LMH _: _ my”!nerwernnou mug“rrrrﬂcrLLla-a‘} -— 4*- [NHLL 1._, :1) mm? arerfwn'near.‘ ~.'-I.l H = of: Hm: r} (i 3+. ['25 pts} A torsion bar is shown hetow. the load mg is appiied in the —a direetion. The bar has a polar moment of inertia J, bending inertia I, cross seetional area A, and diameLer D. Solve using symhois. {a} 1|Write the museums for the stresses on a stress element on the hair at the location of the Rosette strain gage. to; Draw Motif s circle and show on the circle the principle nonnal stresses and the maximum shear stress for a stress element loeated at the rosette gage. {:2} Assume that the strains From the roseth gage are known. Write the equation that is used to compute the principle normal stresses and maximum shear stress ttl terms ofthe measured strains. on At the loeation of the rosette gage. explain if the normal stresses and the normal strains in oaoh direet‘ion will be zero or nonzero. You may use eLressZstrain equations le- help explain. 5". ...
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soln mid term s 07 - Measurement and Instrumentation Lab...

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