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Exam2SP10Soln

Exam2SP10Soln - N ame Section 9:30,Ariyur 11:3{3_Savran ME...

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Unformatted text preview: N ame: Section: 9:30,Ariyur 11:3{3_Savran ME 365 EXAM 2 Thursday March 2 5, 2010 6:30—7:30 pm. FORNEY 6140 PROBLEM POINT DISTRIBUTION SCORE 1 40 points 2 35 points 3 35 points 4 40 points TOTAL 150 points Percentage: 2[3 Total = a Don’t forget your name and please circle your section instructor. 0 Exam is 6 pages including this cover page: make sure you’re not missing any pages. 0 If you use extra pages, indicate on the problem page that you’re continuing onto an extra page. . Pay attention to units. 0 Explain your reasoning. Correct answer with wrong explanation = no credit. Problem 1. Part I The time response of a thermocouple is described by the following first order differential equation: dv 2' +y2Kl’" 622* where y is the output voltage, T is the input temperature, ’t is the time constant, and K is the static sensitivity. a. Write the frequency response function Y/T ofthe thermocouple and its magnitude and phase or argument as a function of angular frequency. at a b. For t=O.1 seconds, K=0.01V/°C, find the angular frequency at which the thermocouple frequency response has a lag of Tit/10 radians. c. For the question in part b, find the angular frequency at which the magnitude of the frequency response is 90% of the magnitude at low frequencies. Part II An accelerometer is described by the following differential equation: 632 d1 , y + b l + Ry : Kr m dfi at where m is the mass, in is the damping coefficient of the dashpoi, and k the spring constant; y is the displacement output of the accelerometer, and X is the displacement ofthe platform on which the accelerometer is mounted. a. For Kle/m, m=1.25e-4kg, and k=SOON/m and damping constant b23563 Ns/rn, calculate the natural frequency and damping ratio. {.5me , WNW 2% # ,,M.-»~ N“ ‘ «- b. What is the resonant frequency ofthe frequency response function Y/X (use the parameters in part a)? Probiem 2. The output of an acceierometer governed by the differential equation: ma {1+bg—3—Vi+/Qa =Kx dz“ dz ‘ is filtered using a iow pass fiiter T dyz + - cit ‘ 3/2 “‘ yi a. Assuming no ioading. write the frequency response function Yz/X b. Write the magnitude and phase ofthe frequency response function in part a. c. What is the roll off rate ofthe Bode magnitude plot onz/X at high frequencies? finialem 3. You are asked to identify a system o. Whose Bode plot 13 shown below. This IS a fitter with both the input at id toe output heing m Voits As you can see, they have to: gotten to git e you the phase phat. So you’fi have to identify the system oniy from the magnitude inf rmatien. Magnitude (dB) 1o" 10" 10‘ 1o2 1:]3 Frequency (rad/sec) a) This 15 a (circie one): @@ / 2nd order system because (fill m the blank) { (21‘; of; i ”A 3L; 23 A (gr/“gee; u b] What is the static sensitivity of this system? 2—3 Gig NEEMS Li: EC) XIX/V c) What is the time constant of this system? we: ‘3 i “fa-i ,oqts. 3 (is 4’. AW," d] What would the missing phase plot took like? Please sketch it beiow. Indicate clearly how the phase behaves at 30w and high frequencies and at the cutoff frequency. 10 1 7134(8) \ Pmbiem 4%. When a system is excitefi wiih. a unit stem ingut, it exhibits {he {Gilawéng respvnse. £8 “J This is a (circle one): 1“ mole: system / é“ ardez‘ system, ‘3. because {ff}! in the biank} "z y ~~ ii 94 ’ ma g What is the static sensitivity? 24 2:; What is the damping ratio (use the 9608 method)? If i s {i {L7 _. "’N x ’\ ~— :wCKND [ N fl. « 1‘ 6 What is the natura} frequency? wézgffl ilflfk “a: E53, : @gflrh. ‘é 2,2, ' W m“; In the Bode plot of this system [éon’t sketch it} would the magnitude have a peak 02‘ not? M: fig mum ...
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