Department of Mechanical and Aerospace Engineering MAE334 - Introduction to Instrumentation and Computers Midterm Examination October 14, 2003 o Closed Book and Notes o Fill in your name on your scoring sheet o Fill in your 8-digit person number on your scoring sheet. o Fill in circle 1 under GRADE OR EDUCATION on your scoring sheet. This is your test number! You will receive a ZERO if you do not indicate your test number. o For each question, choose THE BEST ANSWER and mark the corresponding answer on the scoring sheet. The terms lab 1 and lab 2 will be used throughout the exam. Remember: Lab 1 – Limitations on A/D Conversion Lab 2 – Static and Dynamic Calibration of a Thermocouple1. In lab 2 the static sensitivity of the thermocouple was approximately a. 2.E-6 b. 2.E-2 c. 2.E+2 d. 2.E+4 2. In lab 2 the magnitude of the slope of the linearized error function, Γ(t), was greater for the water to air step input function than for the water to water step inputs. a. True b. False 3. The units of the static sensitivity obtained from the static calibration of the thermocouple in lab 2 needed to process the dynamic calibration data recorded by the Virtual Bench data logger were a. °C/V b. V/°C c. μV/°C d. °C /μV e. none of the above 4. By sequentially increasing the temperature from cold to hot in the static calibration of a thermocouple the hysteresis error is minimized: a. True b. False 5. A 4 bit ADC with an 8 volt input signal range has a finer resolution than a 3 bit ADC with a 2 volt input signal range. a. True b. False 6. The resolution of an ADC is decreased by increasing the gain of the input signal. a. True b. False 7. An ADC resolution specified in terms of signal-to-noise ratio in units of decibels is defined as 20log2M-1, where M is the number of bits of the ADC. a. True b. False 8. What is the maximum voltage that can be resolved without clipping by a bi-polar ADC with a full scale range of 10 volts and a gain of 50? a. 500 b. 10 c. 5 d. 1 e. 0.1 MAE 334 – Midterm Exam, October 14, 2003 2 of 79. The Nyquist criteria is satisfied if the highest frequency in the signal is a. less than twice the sampling frequency b. less than the sampling frequency c. greater than the twice the sampling frequency d. less than half the sampling frequency e. none of the above 10. The slowest sampling frequency given that would avoid aliasing the waveform y(t) = 5sin(12πt) + 8cos(24πt) is a. 12 samples/sec. b. 24 samples/sec. c. 24π samples/sec. d. 48π samples/sec. e. 16 samples/sec. 11. If t is in seconds, the frequency in Hertz of y(t) = 12sin(42πt) is: a. 12 b. 42 c. 42π d. 21 e. none of the above. 12. The binary representation of decimal 11 is: a. 0011 b. 1011 c. 0110 d. 1100 e. none of the above 13. The 4 bit 2’s complement representation of -3 is: a. 1000 b. 0011 c. 1011 d. 1101 e. none of the above 14. The variance is the square root of the standard deviation of a data set? a. True b. False 15. Using the nomenclature from the text book and class, Sx refers to the a. Sample standard deviation b. Standard deviation c. Variance d. Standard error of the fit e. Correlation coefficient MAE 334 – Midterm Exam, October 14, 2003 3 of 716. For a normally distributed data set, as Sx increases a. The 99% confidence interval of the estimation of the true mean gets larger. b. The signal variance gets larger. c. The probability density function becomes wider. d. all of the above e. none of the above Large Step Input Thermocouple Dynamic Calibration in Water01020304050607080900 5 10 15 20 25 30Time (sec)Temperature (C)Temp DataSimulation Figure 1. Data set from Lab 2 dynamic calibration. 17. The approximate time constant, τ, of the thermocouple response plotted in Figure 1 is: a. 2 seconds b. 5 seconds c. 10 seconds d. 20 seconds e. 25 seconds 18. The simulation plotted in Figure 1 would have used this equation to calculate the time history of the temperature response, T(t), immediately following the application of the step input. (select the best answer!) a. (2)/( ) 75 (5 75)tTt eτ−−=−− b. (2)/() 5 (5 75)tTt eτ−−=+ − c. /( ) 75 (5 75)tTt eτ−=+− d. (2)/() 5 70tTt eτ−−=+ e. (2)/( ) 75 (5 75)tTt eτ−−=+− MAE 334 – Midterm Exam, October 14, 2003 4 of 719. A linear regression analysis yields the following equation, 8yx5=+, for a calibration data set with 20 points. If the standard error of the fit, Sxy, is 1. What is the 90% confidence interval? (Use the student’s t-distribution table on the last page): a. ±1.725 b. ±1.729 c. ±1.734 d. ±2.101 e. none of the above 20. To decrease the confidence interval size, CI, in which the predicted dependent variable value should lie we could: a. increase the number of calibration points. b. increase the CI percentage from 95% to 99%. c. decrease the number of calibration points. d. both a. and b. e. both b. and c. 21. A liquid-in-glass thermometer, a thermocouple, a thermistor and an RTD will behave as first order sensors. a. True b. False 22. An over damped second order system will oscillate with a greater amplitude when than the input when forced at the natural frequency. a. True b. False 23. The histogram plot a. gives an indication of the standard deviation of the data set. b. is an approximation of the probability density function. c. is normally distributed for variations due to quantization error. d. all of the above. e. none of the above. MAE 334 – Midterm Exam, October 14, 2003 5 of 7Figure 2. A probability distribution function for an infinate data set. 24. The area under the PDF function plotted in Figure 2 between the dashed lines of width, dx, is the probability that any single measurement will line within that range. a. True b. False 25. The standard deviation of the means, xS, is related to a. the standard deviation of the data set b. the number of points in the data set c. the mean value of the data set d. all of the above e. both a. and b. Table 1. Student's t-distribution table. Student-t Distribution ν 50% 90% 95% 99% 1 1.000 6.314 12.706 63.656 2 0.816 2.920 4.303 9.925 4 0.741 2.132 2.776 4.604 5 0.727 2.015 2.571 4.032 6 0.718 1.943 2.447 3.707 7 0.711 1.895 2.365 3.499 8 0.706 1.860 2.306 3.355 9 0.703 1.833 2.262 3.250 10 0.700 1.812 2.228 3.169 11 0.697 1.796 2.201 3.106 12 0.695 1.782 2.179 3.055 13 0.694 1.771 2.160 3.012 14 0.692 1.761 2.145 2.977 15 0.691 1.753 2.131 2.947 MAE 334 –