Spring ‘11 Lab 6 - System Response Lab 6 - 1Lab 6 - System Response FFoorrmmaatt This lab will be conducted during your regularly scheduled lab time in a group format. I strongly recommend that you rotate roles during the lab. You may ask the lab instructor for assistance if needed, but successful completion of the lab is your responsibility – not theirs! RReeppoorrttss An individual, informal report covering the first lab exercise (First Order System Response) is due from each student by 8:00 AM on Monday, 3/7/11. This required report will count as two homework exercises. An individual, formal report covering the second lab exercise (Second Order System Response) is due from each student by 8:00 AM on Friday, 3/11/11. Do not include any material from the first lab exercise in the formal report. Use Microsoft Word and Excel to create the report. Two “hard” copies (stapled in the upper left-hand corner) must be turned in – one complete copy and one copy without an appendix (marked “English”). In addition, an electronic copy of the report without figures or appendix must be emailed to the course instructor on the due date. Use your complete name as part of the file name for the electronic copy. PPrroocceedduurreess I. First Order System Response Your lab group will build the circuit shown in Figure 1, which will be connected to both the function generator and the National Instruments data acquisition system. A first voltage follower buffers the output from the function generator to the 1st order RC system. The function generator output is connected to the data acquisition system with the orange (Or) and black (Blk) twisted wire pair. A second voltage follower buffers the output from the 1st order RC system to the data acquisition system. The second voltage follower output is connected to the data acquisition system with the yellow (Yel) and black (Blk) twisted wire pair. OrBlkBlk50TTLFunction Generator+-RCOrCh0 HiBlkCh0 Lo YelBlkCh1 HiCh1 Lo+-OrBlkBlk50TTLFunction Generator+-RCOrCh0 HiBlkCh0 Lo YelBlkCh1 HiCh1 Lo+-+- Figure 1. 1st order RC system time constant set-up.Spring ‘11 Lab 6 - System Response Lab 6 - 21. Build the two voltage follower op-amp circuits shown above. The resistance R is nominally 240 k(220 k kin series) and the capacitance C is nominally 0.022 F. Measure and record the actual series resistance and capacitance of the initially installed components for this 1st order RC system. Connect the function generator and data acquisition system as shown. 2. Adjust the function generator to produce an approximately 4 to 6 Hz square wave with an amplitude of about 2 volts peak-to-peak. 3. Set Signal Express to read 1000 samples at 5 kHz (5,000 samples/sec). This will be data set #1. The vertical position setting for both traces should be approximately centered vertically in the screen. 4. You should obtain a pair of traces that are “similar to” those in Figure L5-2. The square wave ("step input" to RC system) comes from the function generator. The exponential (1st order) response curve comes from the output of the 1st order RC system. It is important that the RC system output reach a constant steady-state value, i.e., the output response should “flatten out” after the 1st order exponential rise or decay. If this does not happen with your RC system, check your resistor and capacitor values and your setting for Signal Express carefully. -6-4-202460 0.02 0.04 0.06 0.08 0.1Time, secVoltageIMPORTANT! Figure 2. Input and output waveforms for 1st order RC system. 5. Have the lab monitor check the results from your RC circuit at this point! 6. When the lab monitor “OK’s” your results, save the data shown on the Signal Express screen in Excel. If you cannot open the file in Excel and see the data for plotting (time,Spring ‘11 Lab 6 - System Response Lab 6 - 3input voltage, output voltage), then you have not stored the data correctly from Signal Express. 7. Estimate the experimental time constants from your plotted data. 8. Compute the theoretical time constant for the 1st order RC system from the measurements of the resistance, R and the capacitance, C. Compare to the experimental time constant estimated in Step #7. These values should agree to within ~10%. Note - it is a "good idea" to perform this step in the lab. If your experimental and theoretical time constants are not "close," you need to find out why before you leave the lab! 9. Measure a 0.0047F capacitor, and add it in parallel with the existing 0.022 F capacitor (keep the existing 240 k resistor combination). This will be your second 1st order RC system. 10. Collect a set of data (1000 samples at 5 kHz ) from the second 1st order RC system and save to Excel. This will be data set #2. Outside of lab: 11. The experimental time constant of each 1st order RC systems can be accurately determined from the input and output vs. time plots. Determine the time constants for each of the 1st order RC systems. 12. Clearly and completely show both experimental time constants on separate plots of the experimental data. Show where the step input initially occurred and when the output reaches the t= value. 13. The theoretical time constant of each 1st order RC system can be determined from the measured resistance and capacitance values. Since the values used in the theoretical computation are measured, there will be uncertainty in the theoretical value for time constant. Use the instrument data from your course notes to determine this computed uncertainty. 14. There will be also be uncertainty in the experimental values for time constant due to the inexact knowledge of when the step input occurred and when the RC output value equals the theoretical prediction. 15. Determine whether the theoretical (±uncertainty) time constants and the experimental time constants (±uncertainty) for both 1st order RC systems overlap. If they don’t overlap, give a reasoned engineering explanation.Spring ‘11 Lab 6 - System Response Lab 6 - 1II. Second Order System Response A load cell / differential amplifier circuit will be used to measure the dynamic response of a 2nd order, spring – mass combination. Four different masses will be used to generate four different natural frequencies for the system. The natural frequencies will be used to estimate the spring rate (or spring constant) of the spring. These spring