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    Modeling Scenario
    250

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    193

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    5-014-TwoSpringMass-ModelingScenario
    We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.
    massspring mass dampersprings
    Potential Scenario
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    79

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing
    Modeling Scenario
    213

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    139

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    3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.
    massundampedFree Body Diagramspringstwo springsoscillationspring constantfixed ends
    Potential Scenario
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    40

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    2017-Ben_Finio-Science Buddies – Linear & Nonlinear Springs Tutorial
    This tutorial provides a basic summary of linear and nonlinear springs and their associated equations for force, stiffness, and potential energy.
    spring massstiffnessspringspotential energyforcenonlinear springlinear spring
    Potential Scenario
    208

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    89

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    1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
    Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two compartment open model are discussed.
    LSDcompartmentpharmacokinetics
    Potential Scenario
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    43

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    1994-S_S_Everingham-C_Peter_Rydell-Modeling the Demand for Cocaine
    This is a report prepared for the Office of National Drug Control Policy of the United States Army by the Rand Corporation. The report contains lots of data and builds a two compartment difference equation model.
    drugstwo compartmentcocainedemand
    Potential Scenario
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    90

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    2014-Hrydziuszko-EtAl-Mathematical Two-compartment Model of Human Cholesterol Transport
    We develop a two-compartment mathematical model to investigate cholesterol transport in the circulatory system and its de novo synthesis in the liver.
    metabolic syndromecompartmentcholesteroltwo-compartment modelcholesterol transport
    Potential Scenario
    144

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    59

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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Modeling Scenario
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    332

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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
    Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order
    Modeling Scenario
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    265

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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Modeling Scenario
    228

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    214

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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.
    attritionLanchester modelpredator-predatorN-square Law
    Free Online Textbook
    126

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    51

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    1991-Carmine_Chicone-Ordinary Differential Equations with Applications
    This is a complete text for a graduate level course. Hence there is much theory, but there is a chapter on applications with some sophisticated approaches and high level modeling of motion.
    orbitstwo mass systematommagnetic fieldcoupled penduluminverted pendulumcharged particleKepler motion
    Potential Scenario
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    51

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    1987-Claude-Marmasse-Studies on differential equations of enzyme kinetics-Biomolecular scheme
    The integral curve is compared with the solutions given by the two classical approximations to the problem: it is shown that the steady-state approximation is to be preferred to the rapid equilibrium theory as a general method.
    steady-state modelisoclinesenzyme kinetics
    Article or Presentation
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    40

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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).
    vibrationresonancetuned mass damperpeak frequency responseexcitation
    Technique Narrative
    488

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    163

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    5-012-LinearSystemConjecture-TechniqueNarrative
    Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
    discovery learningconjecturesolutionsubstitution
    Modeling Scenario
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    331

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    7-040-TankInterruptMixing-ModelingScenario
    We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.
    Laplace transforminverse Laplace Transformsalttankmixinginterrupt
    Potential Scenario
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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial administration through the plasma.
    LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration
    Modeling Scenario
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    357

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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery
    Modeling Scenario
    208

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    237

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    5-020-ParacetamolAbsorption-ModelingScenario
    We offer drug absorption data on paracetamol, an analgesic pain reliever, for two different sets of patients, vegetarian and non-vegetarian. Students build a two compartment model for plasma and non-plasma (tissue) compartments of human patients.
    paracetamolanalgesicvegetariannon-vegetarian
    Modeling Scenario
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    298

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    1-006-Financing-ModelingScenario
    We describe two situations, one in which we are saving for a purpose and one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of...
    financesavingsloaninterest ratepayment