Primary and secondary sources | socology | Strayer University

PRIMARY AND SECONDARY SOURCES

Source Types

The fundamental difference between the two kinds of sources is their timing. If your research is based on documentation that comes directly from the period being researched, then it is primary, but if the material you are using is based on someone else’s research, then it is secondary. It cannot be stressed too strongly that the more primary research one uses in their writing, the more compelling your argument. Using primary sources helps you form your own opinion. If you rely on secondary sources, you are relying on someone else’s interpretation of events.You will be required to use at least six sources for each assignment.

Primary Sources

Primary sources provide first-hand testimony or direct evidence about a topic under investigation or a source of information that was created at the time under study.
These records were created by witnesses who experienced the events being documented, often at the very time the event occurred.
- These sources can also include memoirs, autobiographies, and oral histories recorded later by the principals themselves.
Age is an important factor in determining whether a serial publication is a primary or secondary source.
- For example, an article on the Titanic by a staff writer in a recent issue Time should be read as a secondary source, even if the author used primary source materials such as ledgers, diaries, or government documents. An article by a survivor of the sinking would be read as a primary source because it was an eyewitness account.

A primary source is an immediate, firsthand account. Some examples include:

Maps.
Diaries.
Letters.
Memoirs.
Museum exhibits.
Photographs.
Oral histories
Autobiographies.
Presidential library holdings.
Dissertations and theses.
Speeches (transcriptions).
Eyewitness accounts of events.

Secondary Sources

Secondary sources are generally accounts written after the fact with the benefit of hindsight.
Secondary sources are interpretations and evaluations of primary sources and are not evidence, but rather a commentary on, and discussion of, that evidence.
Books are usually considered secondary sources, but writers may use primary source materials such as letters and diaries to write the books themselves. Thus, books can be a rich source of primary sources, especially if you consult the footnotes and endnotes.

A secondary source is one step removed from primary sources, though they often quote or otherwise use primary sources. Secondary sources may cover the same topic but add a layer of interpretation and analysis. Some examples include:

Manuals.
Almanacs.
Textbooks.
Fact books.
Directories.
Guidebooks.
Chronologies.
Bibliographies.
Historical works.
Biographical works.
Commentaries and criticisms.
Monographs, other than fictional works and autobiographies.

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July 1, 2023

SYSEN533

DeterministicModelingandSimulationExam1

1. (25 pts) Thecompound tanksystemshown in Figure1 consistsof asphericaltank ofradius R1and acylindrical tankofdiameterD2. A liquid ofconstantdensityis fed atavolumetricrateF1in intothetopof aspherical tankandvolumetric rateF2in intothetop ofthecylindricaltank. The sphericalandcylindrical tanks interactthrough thepipeconnectingthem.Theflowrates intotheconnecting pipedepend ontheheightsoftheliquid in thetanks. Thevolumetric flowrate outof thesphericaltank

intothepipeis given byF1out =k1

h1 , whilethevolumetric flow rateoutofthecylindricaltankinto

thepipeis given byF2out =k1

h2 whereh1 and h2 arethe heightsoftheliquid in thesphericaland

cylindrical tanks respectivelyandk1 is thecommonvalvecoefficient.Thecylindricaltank alsohas a

drain on theright-hand sidewhich hasvolumetricflowrateF3out =k2

coefficientfortheright-hand sidedrain.

h2 wherek2 is thevalve

a) Obtain a dynamicmodelthatdescribes theheightsoftheliquid in thetanks. Is this a linearornonlinearmodel?

b) For constantinputflow rates, F1in and F2in, analytically determine thesteady-statevaluesofh1 and

h2. Dotheshapesand dimensionsof thetanksaffectthesteady-statevalues?

Notethatyoudonotneedtosolvethedifferential equations for thesteady stateanalysis.

c) Simulatethesystem and plottheheightsoftheliquidin thetanks versustimeforconstantinputflowratesusing thevaluesgiven in thetablebelow.(Run thesimulation for2000sec)

F1in	2.0 ft3/s	F2in	1.0 ft3/s
R1	10.0 ft	D2	20.0 ft
k1	2.0ft5/2/s	k2	3.0ft5/2/s
h1(0)	4.0 ft	h2(0)	4.0 ft

Figure1.Compound TankSystem

2. (25pts) Chaoticsystemsareones forwhich small changes eventuallylead toresults thatcan bedramaticallydifferent. The Rösslersystemisoneofthesimplestsets ofdifferential equationsthatexhibits chaoticdynamics. In addition totheir theoretical valuein studyingchaotic systems,theRösslerequations areusefulin several areasofphysicalmodeling including analyzing chemicalkineticsforreaction networks. Consider thereaction network:

A1+X2X

k-1

X+Y2Y

k-2

A5+YA2

k-3

X+ZA3

k-4

A4 +Z2Z

k-5

whereX,Y, and Z represent thechemical specieswhoseconcentrationsvaryandA1, A2, A3, A4, and A5 arechemicalspecies whoseconcentrationsareheldfixed bylargechemical reservoirs, serving tokeepthe system outofthermodynamicequilibrium.ki andk-i denote theforward and inversereaction rates.Thesystem of differentialequations thatdescribetheconcentrations x, y, and z(for chemicalspeciesX,Y, and Z) are:

dx =-y-zdt

dy =x+aydt

dz =b-cz+xzdt

a) Simulatethis systemfor a=0.380, b=0.300,and c=4.280with initial conditionsx(0)=0.1,

y(0)=0.2, z(0)=0.3. Run thesimulation for200seconds using a fixed-step size algorithm witha stepsizeof0.001seconds.Plottheconcentrationsx, y, andzversustimeononefigurewiththreesubplots. Additionally, in separategraphs, plotthephase-spaceplots:xversus y,xversusz, and yversus z. Finally,makea3-Dplotof xvs yvszusing theMatlab graphics command "plot3"

b) Illustratethesensitivityofthesolution to variations intheinitial conditions byrepeating thesimulation ofpart(a) withx(0)=0.0999and thenwith x(0)=0.1001. (A0.1%changein thevalueoftheinitial condition in either direction.)Keeptheinitial conditions for y(0) and z(0) thesameas inpart(a). Showthesensitivitybysuperimposing theplots forthenew valuesyouobtain forx(t),y(t),and z(t)with theoriginal plots forxvs t,yvs t,and zvs t. In addition,makeplotsof thedifferences:x(t)– xorginal(t) vst,y(t) –yorginal(t) vst, and z(t) –zorginal(t) vs t.

c) Illustratethesensitivityofthesolution to variations inparametervalues byrepeating thesimulationof part(a)withc=4.280001. [Use theoriginal initial conditions from part(a).]Show thesensitivitywith thesamesetof plotsas in part(b).

Whyisthis systemnon-linear?

Qualitatively describethesensitivity toinitial conditions and parametervalues.

3) (25 pts) Acontinuous stir tank reactor(CSTR)is used toproducea product P fromchemicals Aand B.Thereactionis A+BàP. Ais inexcess andtherateof decompositionofBisgiven by:

rb =

k1 x2

+ 2

(1 k2 x2 )

wherek1and k2areconstants and x2is theproductconcentration.Theequations describing thesystemaregiven by:

1 1 2 2

The parameters are: Cb1 =24.9,Cb2=0.1 ,k1=k2= 1,andu1 =u2 = 1.The initial conditions are: x1(0) =10and x2(0)=0.

a) First, simulatetheequation for x1onlysinceitdoesnot depend onx2.Notethesteady-statevaluethatyou find forx1.

b) Inthemodelforx2, initializetheintegrator for x1to thesteady-statevalue you found in part(a) andinitialize x2(0)=0. Run thesimulation for 1000seconds to determinex2(t)and thesteady-statevalueof x2.

c) Repeatthesimulation for x2 using an initial value x2(0)=10. Notethenewsteady-statevalueyoufindfor x2.

d) Bothof thepreviouscasesarestable.Thereis anothersteadystatecorresponding to everything elsebeingthesameand thesteadystates forx2and x1being x2= 2.793and

x1=100.This is an unstablesteadystate.Demonstratethis bysetting theinitialvalueoftheintegratorforx2tox2(0) =2.80andshowthatthesimulation goesto theuppersteady-statevalue.Repeatthesimulationwithx2(0)=2.79 and showthatitgoes tothelowersteady-statevalue.Thismeansthatanysmall fluctuation willcausethesystemtofalltosteadystateofpart(b)or risetothesteady stateof part(c).

e) Demonstratethatthesteadystatewith x2=2.793is unstablebylinearizing theequation forx2aboutthesteady-statevaluesandshowingthatthelinearsystem thatresultsis unstable. Youcan do this by either solving thedifferential equationor by simulating thesystem witha small initial Dx2.

4) (25 pts) Considerthefollowing linear system

G(s)=-8s+6 2s3 +9s2 +13s+6

For this problem, usea unit step input.

a) Createamodel for this systemusingonly integrators and run itfor10seconds.

b) Replacetheintegratorswith discreteintegratorsand investigatetheeffectof forward, backward,and trapezoidal integratorswith sampling timesof0.01, 0.1, and0.2seconds.

Notethatintheconfiguration parametersyouwillneedtospecify thestepsizeand changetheintegratortodiscretestates only.Also,setallof thesampling times inthevarious blocksequal tothediscretesampling time.

c) For each case, comparethetruesolution tothediscretesolution intwo ways:

(i) Plotthetruesolution (in blue) and discretesolution (in red)ona singleplot.

(ii) Plotthedifferencebetween thetruesolution and thediscretesolution.

If youwantto bereallyfancy, usethesubplotcommand toshowboth plotsin asinglefigure.

d) Computeanestimateof theintegral squareerror foreach caseand createa tableofthesedifferences.

e) Whatconclusionscanyoudrawregarding theaccuracyofthedifferentmethodsand step sizes?