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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 Dynamic response”__and the attached file named__“Final data Excel & and frequency screen shots shape”__which has internal 2 folders for both parts to make orginaised for u, and__“Lab setup pictures & “R&C” measurement”__to see our results. - See the lab procedures r done by the doctor for both parts inside outside lab with clarifying everything.
- Then write A Formal lab by meeting all the requirements in the attached file name
__“Formal_Lab_reports”__ - See the good example from the teacher for another attachment that called “Good lab example from the teacher”
**While that, you can use whether EXCEL or MATLAB to do the lab as u like**__Finally, you need to include all the 7 following in the final formal lab__- Objective
- Background
- Experiment
- References
- Results
- Conclusions
- Appendix

Fall 2018
Lab 6 – Dynamic Response
Lab 6-1
Lab 6 – Dynamic Response
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, formal report consisting of two parts must be submitted from each of you. Part I
will consist of a title page and Objective, Background, Experiment, and References sections and
will be electronically submitted to a Turnitin link on your class’s ME 360 Blackboard site. A
professional English grader will grade the quality of the writing in your report. Part II will be
composed of the original Part I with the addition of Results and Conclusions sections, along with
an Appendix. Part II will be submitted electronically through the same Turnitin link as Part I (it
will be a draft revision). In addition, a paper submission of the complete report (Part II as
composed of Part I and additional sections) to the lab TAs will be required. Submission of Part I
to Turnitin will be due at the beginning of your registered laboratory time, the week
following performance of the respective labs. The complete Part II (Part I and additional
sections) will be due at the beginning of the class (12pm) on Monday, November 5 for all
students.
For every twenty-four hour period that you are late in submitting your report, a letter grade will
be deducted from that lab grade. For example, if you hand your report in five minutes after the
deadline, your maximum score is 90/100 for this formal lab; if you hand the report in twentyfour hours and five minutes after the deadline, your maximum score is 80/100 for this formal lab,
etc. At a minimum, all of the information specifically requested in this lab manual should be in
your report. Try to use the following naming convention for your file name for the electronic
copy: ME360_FA18_Formal2_Last name (First letter capitalized)_First name (First letter
capitalize).
Background
A solid understanding of dynamic response is important for mechanical engineers. Measures of
dynamic response include
- time constant (1st-order systems),
- natural frequency and damping ratio (2nd-order systems; not covered in this lab), and
- bandwidth (any order system).
Of course, in order to evaluate a system’s dynamic response, it is first necessary that the timeresponse be captured. To that end, some data acquisition system must be implemented. You will
accomplish the following tasks during the course of this laboratory:
I.
Evaluation of time-constant for a first order system by observing the transient response
You will construct a basic RC circuit on your breadboard. You will then drive this
system with a square wave. Voltage followers will be used to buffer both the input
signal coming from the function generator and the voltage output of the RC circuit. The
Fall 2018
II.
I.
Lab 6 – Dynamic Response
Lab 6-2
two signals will also drive LEDs on your breadboard, such that you may directly (with
your own eyes!) observe (see!) the influence of a system’s time-constant on its output.
Evaluation of bandwidth for a first order system by observing the steady state response
Bandwidth is defined as the frequency at which an output signal drops below 70.7% of
the “low frequency” output. This will be further explained below. You will use sine
signals to drive the circuit constructed in Part I. You will record the input and output
signals, such that you will later be able to determine the signals’ magnitudes and the
corresponding phase shift between the two signals. In addition, you will visually
observe the influence of the signals’ magnitude and phase response using the LEDs on
the breadboard.
Evaluation of time-constant for a first order system by observing the transient
response
As discussed in class, common first-order systems include (among others) a mass sliding on
a viscous surface, a thermal “mass” immersed in different fluids, and basic RC circuits. Of
those three systems, the easiest to construct and test is the RC circuit. To that end, you will
be constructing an RC circuit on your laboratory station breadboard. To prevent loading of
the circuit, you will use load followers to buffer the input and the output signals. You will
also use the load followers to simultaneously drive LEDs such that you will be able to
visually interpret the input and output signals. The circuit that you need to construct is shown
in Figure 1 below. In that figure, the input signal, Vin, is indicated on the intput to the first
load follower and the output signal, Vout, is the output of the second load follower. The
dashed box around the four LEDs is meant to imply that the LEDs are part of the “bar graph”
LED chip. The middle two LEDs are used to indicate the status of the input signal (one will
be fully on when the input signal is +5V and the other will be fully on when the input signal
is -5V). The outer two LEDs correspond to the output signal, one for positive voltages and
one for negative voltages. (In fact, 0.7V is the minimum voltage to drive an LED, so the
LEDs will not be lit for voltages between ± 0.7V.) Also note: the ±12V rail voltages for the
op-amps are not shown, but they are necessary.
220
220
‐
‐
+
+
+
Vin
‐
156k
0.1µF
1µF
0.1µF
1µF
+
Vout
‐
Figure 1. RC circuit with indicating LEDs.
To help you in understanding the circuit, a “Fritzing” breadboard layout of the circuit is
shown in Figure 2. Note that (a) you will be using only four of the ten LEDs on the LED chip
and (b) in Figure 2, some of the LEDs are shown red and some are white; for the chips used
in lab, all LEDs are red. Also, there is a blue “Chiclet” shown connecting the non-inverting
input of the second op-amp and GND. That is the capacitor that, in the laboratory, will be a
Fall 2018
Lab 6 – Dynamic Response
Lab 6-3
deep red color (and will look even more like a Chiclet – don’t eat it). Finally, in Figure 2,
only one capacitor is shown. However, in the lab, you will be using a pair of 1µF capacitors
in parallel, to realize an equivalent capacitance of 2µF. Similarly, the 156k resistor is
composed of a 100k and a 56k resistor in series.
As you go through this first part of the lab, you will be evaluating the sytem’s time-constant
for various combinations of resistors and capacitors. To that end, you should record all
resistance and capacitance values in the table shown at the end of this section of the lab. In
addition, you should record time-histories of the signals using Waveforms and the ‘Scope
software.
Ch1
Ch a0
Ch2
Ch
a1
+12V
+5V
GND
‐12V
Function Generator Signal
Figure 2. Breadboard layout of RC circuit.
1. Construct the circuit shown in Figures 1 and 2. Use the DMM to measure the resistances
of the 100k and 56k resistors and the capacitances of the two 1µF capacitors. RECORD
the exact values that you measure for these components.
2. Test the circuit by MOMENTARILY connecting the +5V rail signal to the non-inverting
input (pin 3) of the first op-amp. When you do that, the left two LEDs should light up.
REMOVE the +5V rail signal before moving to the next step.
3. Use the Waveforms function generator to generate a 0.5 Hz square wave with an
amplitude of ± 5V.
To get the Waveforms function generator up and running, do the following:
- Start Waveforms by double-clicking on the appropriate shortcut on your lab station
PC’s desktop.
- Select “Wavegen” from the menu on the left side of the Waveforms window.
- Change the waveform type to “Square” by using the dropdown menu that is initially
labeled “Sine.”
- Change the frequency and amplitude to 0.5Hz and 5V, respectively, by using the
appropriate text-entry boxes.
Fall 2018
4.
5.
6.
7.
Lab 6 – Dynamic Response
Lab 6-4
- Start the signal output by clicking on the “Run” button.
- Start the oscilloscope function of Waveforms by selecting “Windows,” then
“Waveforms,” and selecting “Scope” from the menu on the left side of the
Waveforms window.
Check the square wave with the oscilloscope to make sure that the signal has a zero mean
(goes from +5V down to -5V) and that its frequency is 0.5 Hz.
Apply the square wave to the input of the circuit shown above. If your circuit is working
properly, the left two LEDs should be lighting together and the right two LEDs should be
lighting together. The two pairs should be alternating as the square wave goes positive
and negative (left-left, then right-right, then left-left, etc.). IT IS IMPORTANT THAT
SCOPE CHANNEL 2 BE CONNECTED TO THE OUTPUT OF THE SECOND LOAD
FOLLOWER, NOT THE INPUT. OTHERWISE, LOADING WILL OCCUR AND YOU
WON’T GET THE FULL AMPLITUDE OF THE OUTPUT.
Use Waveforms to monitor the input and output signals as measured on Channels 1 and
2. The two signals should look like those shown in Figure 3 below. Do you see a pattern
in how the individual pairs of LEDs light? (Does one LED always turn on a little bit
faster than the other in a given pair?) RECORD the input and output signals at a
sufficient sampling rate and for a sufficient time that you will be able to estimate the
time-constant of the system. That is, it would be difficult to estimate the time-constant of
the system using the figure below. However, if you change the system to 250ms/div, or
even 100ms/div, you will be able to zoom in on a single rising portion of the signal and,
as such, make a better estimate of the time-constant.
To make the best estimate of the time-constant, save your data using the “File,” and
“Export” options. You can then bring up the .csv (comma-separated) file in Excel. SAVE
THIS DATA.
Figure 3. Input square wave and RC output with 220k resistor and 2x0.1µF capacitors
in parallel.
8. Modify your circuit by adding a third 1µF capacitor in parallel with the first two.
RECORD this third capacitor’s capacitance. Keep applying the 0.5Hz square wave.
Again, visually observe the response of the outer LEDs (describe how they light) and
Fall 2018
Lab 6 – Dynamic Response
Lab 6-5
RECORD the time response using Waveforms and with a time/div value that will allow
you to estimate the time-constant in Excel.
9. Now, remove the three capacitors and replace them with a single 0.01µF capacitor.
Record that capacitor’s value. Then repeat the observations and time response recording
of Step 8, modifying the time/div value as appropriate.
For each test, record the resistance and capacitance of any circuit elements and the time
response at a time/div level that will make for an accurate estimation of the time constant.
Outside of lab:
Write a description of how the LED turns on and off during the different circuit cases listed
above. Support your observations with plot(s) of the input and output signals. Explain why the
differences occur, in terms of the components used. Your explanation should be quantitative, as
well as qualitative (some math should be involved).
Calculate the theoretical time-constants for the different systems using the appropriate resistor
and capacitor values that you recorded above. Then calculate the time-constant of your
experimental sytem using the time-records of the input and output signals. Compare the two
time-constants. When you include uncertainty in all measurements, do the time-constants
overlap? (Uncertainties should include resistance and capacitance values for the theoretical time
constant and uncertainties due to sampling for the experimental time constant.)
Write a description of how the LEDs light up and use your knowledge of the system timeconstants to explain the particular pattern that can be observed.
Table 1. Data for evaluation of time-constant.
Case
R (k) C1(µF)
R=156k, C=2x1µF
R=156k, C=3x1 µF
R=156, C=1x0.01µF
Change roles in your group at this point.
C2(µF)
C3(µF)
th(s)
exp(s)
Fall 2018
II.
Lab 6 – Dynamic Response
Lab 6-6
Evaluation of Bandwidth for a first order system by observing the steady state
response
1. Put your system back to the original configuration of the 156k resistor and the two 1µF
capacitors in parallel. Switch the function generator output to provide a 0.1 Hz sine wave
with a 5V amplitude (10V peak-to-peak). Check that your signal is zero-mean using the
oscilloscope.
2. Use Waveforms to record at least four full periods of the input and output signals. Make
sure that the sampling rate is sufficiently high to allow for a good estimation of the two
signals’ magnitudes, as well as any time delay between the two signals. The time delay
will be used to estimate the phase difference between the two signals. You may want to
examine your data in Excel during the lab, to be sure that you can predict the amplitudes
of the input and output signals and the phase lag. Carefully observe the lighting patterns
(again) and consider how the recorded data supports the lighting patterns.
Note – you may be seeing a “dead-band” between when one pair of LEDs turns
off and the other pair has not yet turned on. Do you know why it is there?
Consider that an LED doesn’t start to conduct until 0.7V is applied and you will
probably figure it out.
3. Now, increase your frequency to 0.2Hz and repeat Step 2. You may need to adjust your
sampling rate to accommodate the faster signal (faster in the sense that corn syrup flows
faster than molasses – they’re still both slow).
4. Repeat Step 2 for frequencies of 0.25, 0.5 Hz, 1 Hz, 2 Hz, 4 Hz, 8Hz, 16 Hz, and 32 Hz.
Record input and output signals at all frequencies and adjust the sampling rate to ensure
that you capture sufficient data to accuractly estimate the amplitudes of the two signals
and the phase differences between them. As the frequency gets higher, you should
carefully examine the LEDs. What is happening to the LEDs corresponding to the output
signal? Be prepared to explain this in your results. When finished, you should have input
and output records for each of the following frequencies so that you can fill in Table 1
below. Make sure that, for each frequency, you capture the data at a sufficient rate
to be able to estimate the amplitudes and phase accurately!
Outside of lab:
Fill in Table 1 shown below. The linear gain is the ratio of the output amplitude divided by the
input amplitude. The dB gain is 20*log10(G), where G is the linear gain. To calculate the phase
angle, define tin as the time that the input signal passes through 0V and tout as the time that the
output signal next passes through that same value. The time lag between the two signals is then
defined as dt=tout-tin. Divinding dt by the period of the signals, T, gives the time lag as a fraction
of the full period. Since one full period corresponds to 360, you can multiply the result by 360
t t
to get the phase lag. That is, the phase lag, , is given by out in 360 .
T
Next, create four plots of the frequency response in either MATLAB or Excel. The first plot
should be a plot of the linear gain vs. linear frequency (gain on the vertical axis and frequency on
the horizontal). The second plot should be the phase lag (deg) vs. linear frequency. For the third
and fourth plots, the horizontal axes should be frequency, but the axes should use a logarithmic
scale. The vertical axis of the third plot should then be the gain in dB. The vertical axis of the
fourth plot should be the phase lag in degrees (as in the second plot).
Fall 2018
Lab 6 – Dynamic Response
Lab 6-7
The bandwidth of a dynamic system is defined as the frequency at which the output amplitude
drops to 70.7% of the level at “low” frequencies. Also, for a first-order system, the bandwidth is
determined by the frequency at which the phase lag between the input and output goes to 45.
Use your third and fourth frequency response plots to estimate the bandwidth of your system.
1
Finally, for a first-order system, the bandwidth is also given by the formula bw , where is
the system’s time constant. In this case, is given by the product RC. So, calculate the
theoretical bandwidth based on the RC time-constant and compare this to the bandwidth as
evaluated above. In all, you will have three separate methods for calculating the system’s
bandwidth.
Write a description of the LED lighting behavior at the different frequencies. Can you relate the
lighting behavior to the frequency response of the system as presented in your four plots? Think
about the implications of magnitude and phase as functions of frequency and how they are
manifest in the lighting behavior.
Table 2. Frequency response data and results.
Frequency
(Hz)
0.1
0.2
0.25
0.5
1
2
4
8
16
32
Frequency
(rad/s)
Input Amp.
(V)
Output Amp.
(V)
Gain
(linear)
Gain
(dB)
Phase lag
(deg)
Required Sections and Word Limits
Objective – 50 words
Background – 450 words
Experiment – 450 words
Results – 150 words
Conclusions – 100 words
ME 360 Formal Reports
Objective(s) – 50 words or less
Address the questions:
– “What is the purpose of the lab experiment?”
– “What were you trying to accomplish?”
BE CLEAR
You have 15 seconds to convince your
boss why and what you did is important
Do NOT say the purpose was to
– “introduce the student to…”,
– “become familiar with…”, etc.
Background – 450 words or less
Gives information necessary to
understand and appreciate the report.
EDUCATE the reader on
– Relevant equations
– Relevant schematics
– Utility of the technology/subject of the lab
– Specific applications where the
technology/subject of the lab is used in the
“engineering world”
Experiment – 450 words or less
A description of the experimental setup
– dimensions of beams, weights, component
values in op-amp circuits, etc.,
– diagrams (sketches or schematics)
showing all relevant dimensions and/or
component values,
– descriptions of all test equipment used,
– complete schematics of circuits used,
– a brief description of the experimental
procedure, but not a "cookbook recipe"
Experiment (Continued)
The "Experiment" section focuses on the
"how" of your lab experience
Do not duplicate the "Background" section which contains general truths
NOT a cut-and-paste of the lab handout!
Write so that a missing lab partner could
reproduce what you did in the lab!
Results – 150 words or less
Present in concise terms the significant
results of the effort in
– words,
– tables,
– figures:
comparison of actual results to theory, if
appropriate,
an uncertainty analysis and evaluation of its
results, and
an analysis of sources of error (if any) in your
experimental technique
Results
Address any questions specifically
asked in your lab handout
Using tables and figures? They MUST
be discussed or mentioned in the text!
Note - This is the most important
single section of a 360 lab report!
Conclusions – 100 words or less
Should be a short paragraph that
restates the major results and, perhaps
more importantly, interpretations of
those results with numerical values, if
appropriate.
Were the objectives of the lab met?
What can you conclude from the lab?
References – at least three, preferably more
Any material taken directly from another
author must be given proper reference.
You may NOT reference your ME 360
course manual for anything
Using a picture that you didn’t create?
CITE IT in the caption, as well as in the
references
References
Use engineering-quality references
Appendix
– Books, journal papers, and technical
papers
– index / table of contents (typewritten!)
– raw data sheets,
– sets of sample calculations,
May be neatly
– uncertainty analysis
hand-written!
– Manufacturer’s application notes and
“white papers”
Wi ...

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Hello buddy, I am done with all the sections apart from the results and conclusion. Please have a look at this that I have done so far.

Formal Lab 6

Dynamic System Response

Name

Lab Partners

Date

Dynamic Response Lab Report

Objective

The objectives of this lab experiment is to determine the time-constant of a first order system by

observing the transient response and to determine the bandwidth of a first order system by

observing the steady state response by using an RC circuit configured around an op-amp with LEDs

as outputs and square wave or sinusoidal signal of given amplitude and frequency as the input.

Background

When a system (including mechanical system, electrical system, thermal system, fluid system etc.)

can be subjected to a given input and the dynamic response of the system denotes the condition of

that given system in reaction to the input to it. Such a state of the system is time dependent and

therefore, it is usually referred to as a time response for the given system. This time response for a

given system consists of a combination of two states i.e. the steady state response which is the state

of the dynamic system that vary with the input to the system and the transient response which is

the dynamic response of the system that vary with on the given initial conditions for the system.

For any system, by observing the transient response then the time constant can be determined and

also by observing the steady state response then the bandwidth of the system can be determined.

Most systems when considered under system dynamic response can be modelled using differential

equations and therefore the solution of the differential equations gives the two component states of

the system response. Therefore, analysis of the differential equations representing the system gives

the transient response as the homogenous solution of the differential equation and steady state

response as the particular solution of the differential equation.

A system whose response is given by a differential equation has an order which is given by the

highest index in the derivative. When, the system is represented in form of a transfer function (i.e.

the ratio of the output to the input to the system) then the order is given...

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