Name:_____________________ Person Number:_______________ Department of Mechanical and Aerospace Engineering MAE334 - Introduction to Instrumentation and Computers Final Examination December 14, 2005 Closed Book and Notes 1. Be sure to fill in your name and 8 digit person number (starting from the left and with no gaps or hyphens) on side two of the scoring sheet and also on this questioner. 2. Be sure to fill in circle number 1 under the “Grade or Education” box on side two of the scoring sheet. This is your exam number. There are 4 different exams! 3. For each question, choose the best answer and place a mark corresponding to that answer on the machine scoring form. 4. All questions are weighted equally. Failure to correctly complete steps 1 and 2 above will most likely result in a grade of ZERO! MAE 334 – Introduction to Computers and Instrumentation – Final Exam - December 14, 2005- Page 1 of 18-1.500-1.000-0.5000.0000.5001.0000.000 0.500 1.000Time (seconds)Amplitude (volts)1.5001) Add the two 4 bit binary numbers 1100 and 0010. A negative number is in 2’s complement binary representation. a) 14 b) 6 c) 2 d) -2 = 1100 (-4) + 2 e) None of the above 2) With no other knowledge about the voltage signal which was discretely sampled using an ADC and plotted in the graph on the right you can determine the highest frequency in the voltage signal was a) 1 Hz b) 2 Hz c) 3 Hz d) With no other knowledge you have no idea what the input signal freq. was 3) The best signal-to-noise ratio that can be achieved with the analog to digital converters used in the lab is 20 log(4096) decibels. a) True Eq. 7.15 b) False 4) A typical dynamic calibration is used to obtain both the static sensitivity and frequency response characteristics of a sensor. a) True b) False – static sensitivity is obtained from a static calibration 5) Which extraneous variable most contributed to the discrepancy in the PV = constant assumption used in “Lab #4 Studying the Behavior of a Compressed Gas.” a) Quantization error b) Electronic interference noise c) Temperature change of the compressed gas, PVn (polytropic system) d) Pressure transducer accuracy e) Potentiometer accuracy 6) If the sensor output, y(t), is a linear function of the input, y(t) = KF(t), then a) The static sensitivity is frequency dependent b) The sensor could be a thermocouple c) The sensor behaves as a zero-order system d) All of the above e) None of the above MAE 334 – Introduction to Computers and Instrumentation – Final Exam - December 14, 2005- Page 2 of 187) If a system can be modeled with the equation, , where m and cOutputv= mc dT(t)/dtv are constants and T is a function time, t, it is referred to as a first order system. a) True, it is a first order diff. eq. Sensor Response-0.200.20.40.60.811.2-1012345Time/τy(t)Response Step Functionb) False 8) Is the plot on the right representative of a first order system response? (τ is the time constant) a) True b) False, at t/τ = 1, value≈ (2/3)y(∞) 9) If you know the time constant, τ, of a first order system you can uniquely define the frequency response characteristics of the system. a) True b) False 10) If the transfer function magnitude ratio of a first order system is 21/2M( )= 1/[1+()]ωωτ then to avoid aliasing of a fluctuating temperature signal with a range of 1 °C recorded using a thermocouple you could sample at what rate? Given: τ = 1/(2π) seconds and the measurement resolution is 0.1 °C. (Hint: at what frequency is the response of the thermocouple to a 1 °C fluctuation less than the resolution of your measurement device?) a) 99 Hz, 210.1 , [(1/ 0.1 ) 1]2/221/2M( )= 1/[1+ f(f )]ωππ==/2−b) 99 2π Hz c) 2π Hz d) 1 Hz e) None of the above 11) Using the information from the previous question. The output magnitude ratio at 1 Hz is 12M()=ω. a) True, 1/2[(1/(1 1)]21/221/2M( )= 1/[1+()]ωππ=+b) False 12) The total area under a probability density function is a) Related to the variance of the data set b) Always equal to 1 by definition! c) Related to the number of data points d) All of the above e) None of the above MAE 334 – Introduction to Computers and Instrumentation – Final Exam - December 14, 2005- Page 3 of 1813) The standard deviation is equal to the square of the variance. a) True b) False, equals the square root of the variance 14) Approximately 68% of the measurements of normally distributed variable are within one standard deviation of the mean value. a) True, see figure 4.4 b) False 15) If we know the probability density function of a measurement variable then one can a) Figure out the mean value b) Figure out the variance c) Estimate the probability of recording a particular range of values d) All of the above e) None of the above 16) A large data set (N>1000) has a mean value of 9.2 units and a standard deviation of 1.1 units. Determine the range of values in which 50% of the data set should be found, assuming a normal probability. a) 9.2 ±(0.674 x 1.1) b) 9.2 ± ½(0.674 x 1.1) c) ±(9.2 x 0.674) d) None of the above 17) For all of the static calibrations of linear transducers performed in the lab this semester the number of degrees of freedom of the calibration curve was, ν = N – 2, where N is the number of static calibration points collected. a) True b) False Second Order System Response00.20.40.60.811.21.41.61.820 5 10 15Time (seconds)Response (units) MAE 334 – Introduction to Computers and Instrumentation – Final Exam - December 14, 2005- Page 4 of 1818) The Power Spectrum of the second order system response plotted above would have a marked peak at 2 Hz. a) True b) False, period = 2 sec, freq = ½ Hz 19) The time constant of the second order system response plotted above is approximately 0.5 seconds. a) True b) False, second order system don’t have a time constant! It has a rise time of about 0.5 sec. 20) The settling time of the second order system response plotted above is approximately 7 seconds. a) True, it settles to within ±10% in 7 seconds b) False 21) If the response of a system can be modeled with the equation, () ()(0) sin cosAt Ay(t)= y C Bt Bt eB−⎡⎤++⎢⎣⎦⎥, where A, B & C are constants, then it is a) an over damped second order system b) a critically damped second order system c) an under damped second order system, see lab or 3.15a d) None of the above 22) The damped natural