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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=1.25e4kg, 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 “fai ,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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