ExamI-Solutions-enme351-Spring2007

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Unformatted text preview: t / 2 −2t −2t m ) ) o C; o o C; C; C. τ − #% / #% " + 0 , #% =/ +0 " #% ∞ , 1 #% ∞ = 0 = 1 . #\$ ( )0 1 ∴ #% = −" − τ / 2" +1 = " ( − − ) , (ii) What will the measured temperature be if the thermometer reading is taken at t = 2 sec? (a) Tm = 35 o C ; (b) Tm = 48 o C ; o ∴ #% o #% (c) Tm = 57 C ; (d) Tm = 65 C ; =" =" ( ( − − − (e) Tm = 69 o C . Page 4 of 8 −' ) ) , = &3 ' , , Name: __________________________________ Problem 9 [4 points, Bonus] Consider the strain measuring circuit shown in Figure 3. A strain gauge with nominal resistance R is used. The resistance of the gauge changes as a function of the applied strain. The output voltage is directly related to strain. When a load F is applied as shown in Figure 3, the axial strain is given by (a) ε a = 1 V in −2 ; GF V out (b) ε a = 1 V out −2 ; GF V in (c) ε a = 2 V in −1 ; GF V out 2 V in ; GF V out 2 V out (e) ε a = ; GF V in (d) ε a = Figure 3 Strain measurement circuit. 7 9 ∆7 78 5 7 5 7 + 7 + ∆7 7 = 5= 7 + ∆7 = 5 5 = + ∆7 ⇔ 4 + ∆7 7 ∆7 7 5 = 5 5 − #\$ )ε = ( 5 8. 5 − 7 Problem 10 [5 points] A temperature sensor has an input-output relationship given by V(T) = 2T + 0.05T 2 where T is the input temperature to the sensor and V is the output voltage of the sensor. The units of temperature are in oC and the units of the output voltage are in mV. The sensitivity of the sensor at T = 10 oC is (a) (b) (c) (d) (e) K K K K K = 0 mV/ o C ; = 1 mV/ o C ; = 2 mV/ o C ; = 3 mV/ o C ; = 4 mV/ o C ; #\$ 4 # 6= 5 # #= , =( + Page 5 of 8 \$ , # )#= , = + = " %5 , Name: __________________________________ Problem 11 [10 points] Consider the step response of a second order instrument depicted in Figure 4. (a) What is the ringing frequency in rad/sec? \$* 13 12 11 . 10 ( )\$ ( 9 )\$ y(t) [V] .% ') \$ # (: 14 π π ω= = # =π =" ' 8 7 6 5 4 3 # 2 1 0 0 1 2 3 4 5...
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## This document was uploaded on 02/06/2014.

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