ExamI-Solutions-enme351-Spring2007

B what is the value of the steady state output 15 page

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Unformatted text preview: t [sec] 6 7 8 9 10 Figure 4 Step response of a second order instrument. (b) What is the value of the steady state output? .% ') $ $* . ( 15 Page 6 of 8 Name: __________________________________ Problem 12 [15 points] Consider the periodic function y(t) shown in Figure 5. The Fourier series for the function y(t) is given by y(t ) = 10 π sin 2π t 10 4π t 10 6π t 10 8π t − + − + sin sin sin 10 2π 10 3π 10 4π 10 (a) [5 pts] Determine the fundamental frequency (in Hz) for y(t). (b) [10 pts] Plot the discrete magnitude spectrum; clearly label the axes on the plot. Show details. Figure 5 #$ ( % ( : (= 4 #$ = ( = = % % # $ !+ = 4 =4 = ) = ( +4 π ;4 ; " " ' " ( > ( "( ' '( % Page 7 of 8 ( <! += ( % Name: __________________________________ Problem 13 [25 points] Two identical strain gauges with gauge factor GF and nominal resistance R are used to measure strain on a specimen as shown in Figure 6 (a). The two gauges are connected to a bridge circuit as shown in Figure 6 (b). (a) [10 pts] Derive an expression for the output voltage. (b) [5 pts] Is the relationship between the output voltage, Vout, and the change in resistance of the strain gauges linear or nonlinear? Justify your answer. (c) [10 pts] Assume that the change in the resistance of the strain gauges is small compared to R. Derive an expression for the strain εa in terms of Vin, Vout and GF 1 ∆R ). (Hint: ε a = GF R Clearly show details. (a) (b) Figure 6 . %. ) 78 = 78 = 7 + ∆7 &) * $ #$ 4 = 5 78 7 − 5 78 + 7 7 + 78 7 + ∆7 7 − 5 7 + ∆7 7 + ∆7 ∆7 ∆7 7 = 5= 5 + ∆7 7 7 + ∆7 = 4. %$ ∆7 ( ∆7 #$ ? $ 7) $ ( ( 5 5 % ≅ $4* 5 ∆7 % 5 ≠ , ∆7 )$ $ ∆7 7 5 ) ε= ∆7 7 ∆7 8. 7 5 ) 5 = = 5 8. 5 Page 8 of 8...
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