Midterm Exam for Experimental Methods and Measurements | MAE 2381, Exams of Mechanical Engineering

Download Midterm Exam for Experimental Methods and Measurements | MAE 2381 and more Exams Mechanical Engineering in PDF only on Docsity! 1 Last Name: ______________________ First Name:______________________ ID No.:______________ MAE 2381: EXPERIMENTAL METHODS AND MEASUREMENTS Fall 2015 MIDTERM EXAMINATION October 27, 2015 11:00 a.m. — 11:50 a.m. INSTRUCTIONS  This is a closed-book/closed-notes examination. All formulas and constants will be given to you.  This quiz is conducted in accordance with University rules regarding academic honesty.  There is only one correct answer per question/problem (Each problem has 5 choices) 2 INFORMATION THAT YOU MAY NEED  An n-bit digitizer has n2 counts  The signal-to-noise ratio is given in decibels (dB) by the expression noise sig noise sig V V P P SNR 1010 log20log10   The Shannon sampling theorem is given by maxsample ff 2  The Nyquist criterion is given by BT T B N 2 1 2   The relationship between frequency f and the angular frequency  is f 2  The frequency resolution for a sample of N datapoints sampled at a rate of sf is given by N f f s  Folding diagram 5         2/1222 21 1 nn M     and                2 1 1 2 tan n n     t/ 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 sKx y te 5% settling time rise time error fraction Response of 1st order system to a step excitation dB  0.001 0.01 0.1 1 10 100 M() 0.01 0.1 1 P h a s e , ta n -1 (   ) , d e g -80 -60 -40 -20 0 -25 -20 -15 -10 -5 0 -20 dB/decade Frequency response of 1st order system / n 0.01 0.1 1 10 0.01 0.1 1 D e c ib e ls 10 3 -3 -10 -20 -30 -40  M  = 0 0.1 0.2  = 0.65 0.707 5 2 10 1 0.3 Frequency response of 2nd order system 6 For each problem, mark the most appropriate or correct answer in the corresponding box 1. ONLY ONE of these is considered to be ethical conduct in data acquisition and analysis protocol: a. Adjust data to fit theory through manipulating the offset and gain. b. Throwing data away because they “do not look right.” c. Adjust the offset and gain to make best use of the dynamic range of an analog-to-digital converter. d. Adjust the data so that the r2 value is close to but not equal to one. e. Perform only one experiment and calling it “typical.” 2. One of the following is FALSE regarding a multiplexed digital data acquisition system: a. It allows multiple channels of data to be gathered b. There is a time delay between the channels c. Increasing the number of channels decreases the maximum sampling rate d. The data cannot be filtered to prevent or minimize aliasing e. The incoming signals in general must be conditioned before they can be digitized 3. One of the following is NOT one of the steps of the experimental test plan: a. Tolerance design plan b. Data reduction plan c. Parameter design plan d. Documentation of results e. All of the answers above are the steps in experimental test plan. 4. One of the following is FALSE regarding good practice in gathering data a. Ensure that the data acquisition chain is properly shielded against electromagnetic interference b. Ensure that the instruments are calibrated c. Ensure that the sampling rate conform to Shannon’s sampling theorem d. Ensure that the bandwidth satisfies the Nyquist criterion e. Ensure that the instruments possess linear behavior a b c d e a b c d e a b c d e a b c d e 7 5. This problem involves acquisition of a weak signal. Suppose that it is necessary to resolve 160 V with a 12 bit digitizer operating 0 –10 V. This can be achieved by amplifying the signal by a. Amplifying the signal 10 times b. Amplifying the signal 20 times c. Inverting the signal 10 times d. Inverting the signal 20 times e. Oversampling the signal twice 6. Which of the following is False about digital signals a. They exist at a discrete value in time. b. Digital signal provides a quantized magnitude at discrete time. c. Particularly useful for modern day data acquisition and processing. d. Quantization assigns a single number to represent a range of magnitude of a digital signal. e. Digital signals can also be understood as a representation of information contained by a continuous signal but at discrete time. 7. ONE of the following is NOT acceptable practice when it comes to calibrating an instrument a. Calibrate the instrument with one value of input b. Ensure that the correlation coefficient 2r has a value that is close to 1 c. The input should be a secondary standard whenever possible d. After calibration, the instrument should be protected from any further adjustments e. The power supply of a passive transducer must be stable, i.e., it must not vary with time 8. ONE of the following is NOT true regarding methods to improve signal quality a. Instrumentation cables should be shielded b. Amplification helps in improving SNR. c. Filtering to accept only the useful bandwidth will improve SNR. d. The signal must be converted to a voltage. e. Optical fibers may be helpful in areas where there is strong electromagnetic interference. a b c d e a b c d e a b c d e a b c d e 10 17. Only ONE of the following is true. Increasing the bit count of a digitizer (e.g., from 12 bit to 14 bit) a. It allows for better temporal (time) resolution. b. It reduces noise. c. It allows for better amplitude resolution. d. It prevents aliasing. e. It improves linearity. 18. ONE of the following is FALSE regarding instrumentation characteristics when modeled as a dynamical system a. A complicated signal can be viewed as an infinite sum of sines and cosines. b. If I need to characterize the speed of a first-order system, I will want to look at the value of the time constant. c. If I need to characterize the speed of a second-order system, I will want to look at both the value of the damping ratio and the undamped natural frequency. d. A first-order system has infinite bandwidth. e. Instruments are generally linear, i.e., doubling magnitude of the input will double the magnitude of the output. 19. ONE of the following statements is FALSE about a second-order instrument. a. It is so called because the system dynamics can be modeled as a mass- damper-spring system. b. A large value of the undamped natural frequency can be associated with a large bandwidth. c. It will display an exponential rise if subjected to a step input from a low to a high value. d. Ringing occurs if the damping ratio is less than one. e. It is desirable to have a damping ratio just below one so the instrument can rise to the final state faster than if the damping ratio is one. 20. The response of a second order device is given by the plot shown in Figure 1.Using the provided information, determine the rise time and the settling time of the device. a. 0.23 s ; 0.984 s b. 0.5 s; 0.984s c. 0.5 s; 0.8 s d. 0.23 s; 0.81 s e. 0.5s ; 1.2 s a b c d e a b c d e a b c d e a b c d e 11 Figure 1: Response of a second order system due to step input. 21. A second-order instrument is used to measure square pulses of 1 s pulse separation as shown 1 second 1 second 1 second The instrument has an undamped natural frequency of 10 Hz, a damping ratio of 0.72 and a static sensitivity of one. One of the following is the MOST APPROPRIATE response of the instrument a. 1 second 1 second 1 second b. 1 second 1 second c. 1 second 1 second 1 second d. 1 second 1 second 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 4 R e sp o n se , V Time, s a b c d e 12 e. 1 second