Science
“Position, Velocity, and Acceleration lab” technical writing to complete a professional Control lab report

Question Description

Remember before u handle this work, this work is so important to me, so i will revise it many times before i turn it in and I will rate u depend on your work quality such as providing correct and full response and meet all requirements in the attached instructions. Please avoid the Lack of depth in your response and plagiarism bcz I’ll check it with the ((Turn it in website.))

I need the following:

  • Send it me as WORD document not a handwritten scanned document
  • See the main lab and the attached file named “3 parts data” to see our excel results & another file named "to fill in blank values" to see the lab values.
  • Then write A professional lab by meeting all the requirements for all 3 parts in the main lab file “named (Lab 7 – Position, Velocity, and Acceleration)

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Fall 2018 Lab 7 – Position, Velocity, and Acceleration Lab 7-1 Lab 7 – Position, Velocity, and Acceleration Format This lab will be conducted during your regularly scheduled lab time in a group format. You may ask the lab instructors for assistance if needed, but successful completion of the lab is your responsibility. Report An individual, informal report is due from each student at the beginning of the next lab (Lab 8). Background Position, velocity, and acceleration measurements are of obvious importance to mechanical engineers. To learn more about these measurements, you will do the following during this laboratory: I. Calibration of a linear potentiometer and measurement of displacement. You will be provided a linear potentiometer; a potentiometer where the wiper position on the potentiometer changes with the linear (translational) movement of a shaft. You will calibrate the potentiometer by determining the change in output voltage as a function of shaft displacement. You will then use the calibrated device to measure the length of objects in the 360 laboratory. II. Measurement of rotational speed using a proximity sensor and an incremental encoder. You will be provided a laboratory test-stand with a DC motor and the associated motor driver. You will then measure the motor shaft speed using a proximity sensor and a toothed-gear and then with an incremental encoder. In your laboratory report, you will compare the two methods for measuring shaft speed. III. Measurement of beam vibration using a piezoelectric accelerometer. You will be provided an accelerometer and accelerometer signal conditioner. You will then use the combination to measure the vibration of a mass-ended aluminum beam clamped to the lab station. The acceleration data will be used to determine the natural frequency of the mass-ended beam with two different sets of masses on the beam. In turn, you are to use the natural frequency of the beam to estimate the beam stiffness. In your report, you must compare the measured and theoretical beam stiffnesses. Because there are three parts to the lab, you will be rotating among different laboratory workstations. You will have approximately 45 minutes to make all measurements at a given test stand before rotating to the next workstation. As such, please be sure to stay focused and on-task during the laboratory. Fall 2018 I. Lab 7 – Position, Velocity, and Acceleration Lab 7-2 Position Measurement You will be provided a linear potentiometer similar to the device shown in Figure 1 below. As typical with potentiometers, there will be three wires coming out of one end of the “pot:” an orange, a gray, and a yellow wire. The orange and gray wires are the “ends” of the potentiometer. The resistance between those two points should not change with the pot stroke. The yellow wire is attached to the potentiometer wiper. The resistance between the yellow wire and the orange wire should change as the shaft of the pot is moved relative to the pot body. If that resistance increases, then the resistance between the yellow wire and the gray wire should decrease accordingly. You will also find a set of digital calipers at your lab workstation. A similar set of calipers is shown in Figure 2 below. Figure 1. Linear potentiometer (Omega). Figure 2. Digital calipers (Omega) 1. Use the DMM and the calipers at your lab station to make the following measurements: a. Total potentiometer resistance as measured betweeen orange and gray wires: _________________ b. Resistance between yellow and gray wires with shaft fully retracted: _________________ c. Resistance between yellow and orange wires with shaft fully retracted: _________________ d. Resistance between yellow and gray wires with shaft fully extended: _________________ e. Resistance between yellow and orange wires with shaft fully extended: _________________ f. Full extension length of shaft: _________________ 2. Plot the resistances between the yellow and orange wires and between the yellow and gray wires as functions of shaft stroke using two of the measurements made in (1) above. Determine the two equations that relate the yellow-orange resistance and the yellow-gray resistance as functions of potentiometer stroke. Fall 2018 Lab 7 – Position, Velocity, and Acceleration Lab 7-3 3. Using the digital calipers as a guide, move the potentiometer shaft to the half-extension position. In that position, measure the yellow-orange and yellow-gray potentiometer resistances. Yellow-orange:___________________ Yellow-gray:_____________________ Question: do the measurements made in (3) correlate with the graphs and equations determined in (2)? If not, can you explain why not? Consider the possibility of saturation; that is, the change in resistance stopping beyond a certain point, even if the shaft of the pot keeps moving. 4. Connect the orange wire to +5V and the gray wire to GND on your breadboard. Then, connect your breadboard to the power supply at your lab station. 5. Connect the Channel 1 input of your Analog Discovery Kit 2 (ADK2) to measure the voltage of the yellow wire on the potentiometer. Do not forget to connect the Ch1 black lead to GND on the breadboard. Observe the potentiometer output voltage (as indicated on the yellow wire). See if there is any saturation that you can see on the potentiometer (the voltage maxes/mins out before the shaft reaches max/min extension). 6. Using a DMM and the calipers, measure the voltages and shaft positions for the linear range of operation of the pot. The “start” and “end” positions are the points where the voltage starts to change with shaft movement and then stops changing with shaft movement. Start position:_____________ Start voltage:____________ End position: _____________ End voltage: ____________ 7. Now make a plot of the voltage vs. shaft position and predict the voltage halfway between the start and end positions. Vhalf,pred:__________________ 8. Move the pot shaft to the halfway point indicated in (7) and measure the voltage. How does it compare to the predicted voltage from (7)? Vhalf,act:___________________ Fall 2018 II. Lab 7 – Position, Velocity, and Acceleration Lab 7-4 Angular Velocity Measurement This section of the laboratory will examine three different methods for measuring the rotational speed of a motor’s shaft. The different sensors that you will use are: 1. Optical Tachometer 2. Incremental Encoder 3. Magnetic pickup These are all shown in Figure 3 below. In the first example, a handheld tachometer is pointed at an optical reflective tape on the shaft coupling. The shaft speed in rpm is read directly off of the display on the front of the tachometer. In the second example, a commercial incremental encoder is used. It has a resolution of 360 slots per revolution and is attached to the end of the DC motor/tachometer. The output of this device can be read with the Waveforms oscilloscope. To convert that reading into the motor speed in rpm, use the following formula: Motor' s 60 sec 1 rev rev slots . * * = min sec 360 slots min Finally, a circular plate with ferrous metal “gear-teeth” has been installed on the shaft of the motor and is used to generate pulses as the teeth pass an external, fixed magnetic pickup coil. There are 30 teeth on the plate and thirty “spaces.” As such, 30 pulses are generated for each revolution of the plate. Those pulses are translated into the speed in rpm, which can be read on the readout at the front of the experimental setup. The process for testing these rotary velocity transducers is as follows: 1. Set the speed controller to a desired (low) setting. 2. •⇒Measure the rotational speed of the shaft using each of the transducers listed above: • • • Handheld tachometer (direct reading in RPM) Incremental encoder frequency in Hz from Waveforms oscilloscope. Make sure there are between 5 and 20 complete cycles on the screen. Magnetic gear pickup readout (direct reading in RPM) 3. Change the speed setting and repeat step #2. 4. •⇒Continue step #3 until at least 10 different motor speeds (including the maximum speed) have been tested and the data has been recorded for the report. •⇒Outside Lab: 5. Treat the angular velocity from the magnetic gear pickup readout as ideal (ωideal) and plot the other 2 directly measured speeds (ωhandheld, ωencoder) on the vertical axis of one plot. 6. Plot the deviations (ωhandheld – ωideal) vs. ωideal and (ωencoder – ωideal) vs. ωideal on a second plot. Fall 2018 Lab 7 – Position, Velocity, and Acceleration Lab 7-5 Handheld tachometer (point here) Incremental Encoder Magnetic gear pickup Connections for Encoder Motor speed controller Magnetic gear pickup readout Figure 3. Velocity sensors and DC motor controller. III. Vibration Measurement with Accelerometers As discussed in class, accelerometers are perhaps the most widely used sensors in the field of vibration measurement. As you will see in the lab, they are quite easy to use, provided you have the appropriate signal conditioning equipment. For this portion of the lab, you will be measuring the acceleration response of a mass-ended, cantilevered, aluminum beam. If the end-mass is significantly larger than the mass of the beam, then as a first approximation, the system can be treated as a second-order mass-spring-damper system. The natural frequency of such a system is given by the equation K 3EI , K= 3 , ωn = M end + 0.24 M beam L where E is the elastic modulus of aluminum, I is the cross-sectional inertia of the beam, and L is the length from the base of the beam to the center of the mass at the end. If the beam is pulled to a non-equilibrium position and released, then the beam displacement ( ) response will be x (t ) = x0e −ζωnt sin ωn 1 − ζ 2 t . If you take the second derivative of that expression, you will see (some algebra later) that the acceleration response of the beam will also be a decaying sine with the same frequency. As such, if you measure the frequency of the acceleration signal, you will be measuring the damped natural frequency which, for lightly damped systems, is almost the same as the natural frequency. You can also use the log-decrement method on the acceleration response to get an approximation of the system damping ratio. You will find a mass-ended, cantilevered beam clamped to the lab bench. An accelerometer will be attached to the end-mass; it is mounted using a synthetic wax (as opposed to bee’s wax, which was one of the original accelerometer mounting adhesives). A thin layer of wax is all that is Fall 2018 Lab 7 – Position, Velocity, and Acceleration Lab 7-6 necessary; thicker layers allow for compliance between the device under test and the accelerometer itself (which is a fancy way of saying that a thicker layer may act as an additional spring-damper between the accelerometer and the mass to which it is attached). The accelerometer will be wired to an XDCR (“transducer”) input on an ICP (integrated circuit piezoelectric) signal conditioner (some lab stations will have multi-channel ICP signal conditioners). The signal conditioner will have three gain settings: x1, x10, and x100. If a 10mV/g accelerometer is plugged into the ICP signal conditioner and that channel’s gain is set to x10, then the output voltage on that signal conditioner will be 100mV/g, where one “g” is one “gravity,” also known as an acceleration of 9.81m/s2 or 32.2ft/s2. 1. Measure the distance from the edge of the lab bench (where the beam is clamped) to the center of the mass clamped to the end of the beam (a mass is clamped to the end of the beam and the beam, in turn, is clamped to the table, so two clamps are in use). L=______________ 2. Use a BNC-BNC cable to connect the appropriate signal conditioner output to Channel 1 on the Analog Discovery Kit 2. Run the Waveforms software on your lab PC and set the oscilloscope to run continuously. Gently pluck the end of the beam and observe the resulting acceleration signal on the oscilloscope. Select the appropriate V/div vertical setting so that you will be able to see all of the acceleration signal (you will be able to see all of the peaks and valleys in the response). Select the appropriate s/div time setting so that you can see at least eight periods of the signal. 3. Pluck the beam again and, at the same time, record a single trace of the oscilloscope data. Save that data in a .csv file. Open that file in Excel and verify that you can observe at least eight periods of the signal with sufficient time and voltage resolution so as to get a good idea of each period’s peak value and the time that it occurs. 4. Remove the mass from the end of the beam. Use the scale at your lab station to measure the mass of the end-mass (include the clamp used to hold the end-mass on the end of the beam). Mend-mass=_____________ 5. Apply a different mass (say twice or half the original amount) to the end of the beam. Repeat steps 3 and 4. Outside of Lab: 6. Estimate the two different natural frequencies measured in the lab (in steps 3 and 5). 7. Use the two different natural frequencies and the two different known masses to obtain the approximate stiffness of the beam. In your calculations, you should consider the mass of the beam; you can estimate that value if you know the cantilevered length of the beam, its cross-sectional area, and the density of aluminum. 8. Compare the measured stiffness of the beam to the theoretical stiffness listed in the equation on the previous page. How do the two compare? You do NOT need to include uncertainty in your analysis. 9. For each of the two tests, estimate the damping ratio of the beam using the log-decrement method outlined in the class notes. Use the damping ratio and the theoretical natural frequency as listed on the previous page to estimate the theoretical damped natural frequency. Compare that value to the measured natural frequencies as estimated in (6) above. ...
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Final Answer

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Potentiometer Resistance

Potentiometer Stroke

11.32
2.37

0
148

Between Yellow and Gray
Potentiometer Resistance

Potentiometer Stroke

2.4
11.32

0
148

Potentiometer Resistance (kΩ)

Between Yellow and Orange

Potentiometer Resista

15

10

5
y=
0
0

50

Shaft Lenth (mm)

Voltage vs Shaft Po
6

Output Voltage
2
147

0
5

5

Voltage, V (v)

Shaft Position

4
3
2
1
0
0

20

40

Potentiometer Resistance vs Stroke
y = 0.0603x + 2.4
R² = 1
Between Yellow and Orange
Between Yellow and Gray
y = -0.0605x + 11.32
R² = 1
100
Shaft Lenth (mm)

150

200

Voltage vs Shaft Position
y = 0.0345x - 0.069
R² = 1

40

60

80

100

Shaft Position, L (mm)

120

140

160


#Digilent WaveForms Oscilloscope Acquisition
#Device Name: Discovery2
#Serial Number: SN:210321A1A597
#Date Time: 2018-10-31 18:32::20.576
Time (s)
-0.025
-0.02499
-0.02499
-0.02498
-0.02498
-0.02497
-0.02496
-0.02496
-0.02495
-0.02494
-0.02494
-0.02493
-0.02492
-0.02492
-0.02491
-0.02491
-0.0249
-0.02489
-0.02489
-0.02488
-0.02488
-0.02487
-0.02486
-0.02486
-0.02485
-0.02484
-0.02484
-0.02483
-0.02483
-0.02482
-0.02481
-0.02481
-0.0248
-0.02479
-0.02479
-0.02478
-0.02477
-0.02477
-0.02476
-0.02476

Channel 1 (V)
Channel 2 (V)
0.007106 -0.00034
0.010782 -0.00034
0.007106 -7.15E-06
0.010782 -7.15E-06
0.007106 -0.00034
0.007106 -0.00034
0.007106 -0.00034
0.010782 -0.00034
0.010782 -0.00034
0.007106 -0.00034
0.007106 -0.00034
0.007106 -7.15E-06
0.007106 -0.00034
0.014458 -0.00034
0.007106 -7.15E-06
0.007106 -7.15E-06
0.007106 -0.00034
0.007106 -0.00034
0.007106 -7.15E-06
0.007106 -0.00034
0.010782 -0.00034
0.007106 -0.00034
0.007106 -7.15E-06
0.007106 -0.00034
0.010782 -0.00034
0.007106 -7.15E-06
0.007106 -0.00034
0.007106 -0.00034
0.007106 -0.00068
0.007106 -0.00068
0.007106 -7.15E-06
0.007106 -0.00034
0.007106 -0.00034
0.007106 -0.00068
0.007106 -0.00034
0.010782 -0.00034
0.010782 -0.00034
0.007106 -0.00068
0.007106 -0.00034
0.010782 -0.00034

Magnetic Reading 12
visual
40

-0.0251

Time 1
Time 2
Period (T)
slots/s
speed

-0.025

0.024925
0.022065
0.00286
349.6503
58.27506

-0.02475
-0.02474
-0.02474
-0.02473
-0.02473
-0.02472
-0.02471
-0.02471
-0.0247
-0.02469
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-0.02468
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-0.02467
-0.02466
-0.02466
-0.02465
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-0.02458
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-0.02456
-0.02456
-0.02455
-0.02454
-0.02454
-0.02453
-0.02453
-0.02452
-0.02451
-0.02451
-0.0245
-0.02449
-0.02449
-0.02448
-0.02448
-0.02447
-0.02446

0.007106
0.010782
0.007106
0.007106
0.007106
0.007106
0.007106
0.007106
0.010782
0.007106
0.003431
0.007106
0.010782
0.007106
0.003431
0.007106
0.007106
0.003431
0.007106
0.007106
0.007106
0.007106
0.007106
0.010782
0.010782
0.010782
0.010782
0.007106
0.010782
0.007106
0.010782
0.010782
0.007106
0.007106
0.007106
0.007106
0.007106
0.010782
0.010782
0.010782
0.007106
0.007106
0.010782
0.010782
0.010782
0.007106
0.007106

-0.00068
-0.00068
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00068
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00068
-0.00034
-0.00034
-0.00034
-7.15E-06
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00068
-7.15E-06
-0.00034
-7.15E-06
-0.00034
-0.00034
-7.15E-06
-0.00034
-0.00034
-0.00068
-0.00068
-0.00034
-0.00034
-0.00034
-0.00068
-7.15E-06
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034

-0.02446
-0.02445
-0.02444
-0.02444
-0.02443
-0.02442
-0.02442
-0.02441
-0.02441
-0.0244
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-0.02438
-0.02438
-0.02437
-0.02436
-0.02436
-0.02435
-0.02434
-0.02434
-0.02433
-0.02432
-0.02432
-0.02431
-0.02431
-0.0243
-0.02429
-0.02429
-0.02428
-0.02428
-0.02427
-0.02426
-0.02426
-0.02425
-0.02424
-0.02424
-0.02423
-0.02423
-0.02422
-0.02421
-0.02421
-0.0242
-0.02419
-0.02419
-0.02418
-0.02417
-0.02417

0.010782
0.010782
0.007106
0.010782
0.010782
0.007106
0.010782
0.003431
0.007106
0.010782
0.010782
0.010782
0.007106
0.010782
0.010782
0.007106
0.007106
0.007106
0.010782
0.007106
0.841487
3.245386
4.318686
4.708309
4.847985
4.906796
4.921499
4.925175
4.925175
4.921499
4.917823
4.914148
4.910472
4.906796
4.906796
4.906796
4.899445
4.899445
4.899445
4.895769
4.895769
4.895769
4.895769
4.895769
4.892093
4.895769
4.895769

-0.00034
-7.15E-06
-7.15E-06
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-7.15E-06
-0.00034
-7.15E-06
-0.00034
-7.15E-06
-7.15E-06
-0.00034
0.009346
0.034064
0.041413
0.040076
0.036068
0.03206
0.028051
0.024377
0.021037
0.018364
0.015692
0.013688
0.012018
0.010348
0.009012
0.007676
0.006673
0.006005
0.005003
0.004669
0.003667
0.002999
0.002999
0.002331
0.001997
0.001997
0.001663

-0.02416
-0.02416
-0.02415
-0.02414
-0.02414
-0.02413
-0.02413
-0.02412
-0.02411
-0.02411
-0.0241
-0.02409
-0.02409
-0.02408
-0.02407
-0.02407
-0.02406
-0.02406
-0.02405
-0.02404
-0.02404
-0.02403
-0.02403
-0.02402
-0.02401
-0.02401
-0.024
-0.02399
-0.02399
-0.02398
-0.02398
-0.02397
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-0.02394
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-0.02393
-0.02392
-0.02392
-0.02391
-0.02391
-0.0239
-0.02389
-0.02389
-0.02388
-0.02388

4.892093
4.895769
4.895769
4.892093
4.892093
4.892093
4.892093
4.892093
4.888418
4.895769
4.895769
4.892093
4.892093
4.892093
4.892093
4.895769
4.892093
4.895769
4.892093
4.895769
4.892093
4.895769
4.892093
4.895769
4.895769
4.895769
4.899445
4.899445
4.895769
4.895769
4.895769
4.895769
4.895769
4.895769
4.899445
4.895769
4.895769
4.899445
4.892093
4.895769
4.895769
4.899445
4.899445
4.895769
4.895769
4.899445
4.892093

0.001329
0.000995
0.000661
0.000661
0.000661
0.000327
0.000327
0.000327
0.000327
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-7.15E-06
-0.00034
-0.00034
-7.15E-06
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-0.00034
-7.15E-06
-0.00034
-0.00034
-0.00034
-7.15E-06
-7.15E-06
-0.00034
-0.00034
-0.00034
-7.15E-06
-0.00068
-0.00034
-0.00034
-0.00034
-0.00034

-0.02387
-0.02386
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-0.02384
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-0.02382
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4.895769 -0.00034
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4.899445 -0.00034
4.895769 -0.00034
4.899445 -0.00034
4.895769 -0.00034
4.899445 -0.00034
4.899445 -0.00034
4.899445 -0.00068
4.899445 -0.00068
4.895769 -0.00034
4.895769 -7.15E-06
4.892093 -7.15E-06
4.899445 -0.00034
4.895769 -0.00034
4.895769 -0.00034
4.895769 -0.00034
4.895769 -0.00034
4.895769 -0.00034
4.895769 -0.00034
4.895769 -0.00068
4.895769 -0.00034
4.895769 -0.00068
4.895769 -0.00034
4.895769 -0.00068
4.892093 -0.00034
4.895769 -0.00068
4.895769 -0.00034
4.899445 -0.00034
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Chart Title

-0.025

-0.0249

-0.0248

-0.0247

-0.0246

-0.0245

-0.0244

0.016
0.014
0.012
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0.002
0
-0.0243

#Digilent WaveForms Oscilloscope Acquisition
#Device Name: Discovery2
#Serial Number: SN:210321A1A597
#Date Time: 2018-10-31 18:34::03.114
Time (s)
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Channel 1 (V)
Channel 2 (V)
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magnetic
Visual

176
176.2

-0.02505

Time 1
Time 2
Period (T)
slots/s
speed

-0.025

0.024994
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0.003431
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4.903121 -0.00034
4.899445 -7.15E-06
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4.899445 -0.00068
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4.903121 -0.00068
4.903121 -0.00068
4.903121 -0.00034
4.906796 -0.00068
4.903121 -0.00034
4.903121 -0.00034

Chart Title
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
-0.02495

-0.0249

-0.02485

-0.0248

-0.02475

0
-0.0247

#Digilent WaveForms Oscilloscope Acquisition
#Device Name: Discovery2
#Serial Number: SN:210321A1A597
#Date Time: 2018-10-31 18:34::47.890
Time (s)
-0.025
-0.02499
-0.02499
-0.02498
-0.02498
-0.02497
-0.02496
-0.02496
-0.02495
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-0.0248
-0.02479
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-0.02477
-0.02477
-0.02476
-0.02476

Channel 1 (V)
Channel 2 (V)
0.007106 -0.00335
0.007106 -0.00268
0.007106 -0.00268
0.003431 -0.00235
0.007106 -0.00168
0.007106 -0.00201
0.007106 -0.00134
0.010782 -0.00134
0.010782 -0.00101
0.043863 -0.00068
2.050788 0.021371
3.859226 0.038072
4.546579 0.04041
4.79285 0.037404
4.884742 0.03373
4.914148 0.029721
4.925175 0.025713
4.925175 0.022039
4.925175 0.019367
4.921499 0.017028
4.917823 0.014356
4.914148 0.012352
4.910472 0.011016
4.906796 0.009346
4.903121 0.00801
4.899445 0.007007
4.888418 0.005671
4.873715 0.005003
4.884742 0.004669
4.895769 0.004001
4.895769 0.003333
4.899445 0.002665
4.895769 0.002331
4.899445 0.001663
4.903121 0.001663
4.899445 0.001329
4.899445 0.000995
4.899445 0.000661
4.899445 0.000995
4.895769 0.000661

magnetic
visual

370
370.5

-0.0252

Time 1
Time 2
Period (T)
slots/s
speed

0.024688
0.024271
0.000417
2400.96
400.1601

-0.025

-0.02475
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