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    Modeling Scenario
    261

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    210

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    3-105-FrequencyResponse-ModelingScenario
    We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
    transient dynamicscircuitspring massdriverfrequency responseamplitudesteady state
    Article or Presentation
    177

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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
    Modeling Scenario
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    698

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    4-023-MysteryCircuit-ModelingScenario
    Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.
    filterscircuitRLC circuitKirchhoffvoltagegaindriver
    Potential Scenario
    155

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    75

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    2017-David_Morin-Oscillations
    So needless to say, an understanding of oscillations is required for an understanding of waves.
    dampingfrequency responseresonanceoscillationbeatsunderdampingharmonic oscillatorsover dampingcritical damping
    Potential Scenario
    161

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    64

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    2011-Kenny_Harwood-Modeling a RLC Circuit Current with Differential Equations
    This paper gives an abbreviated description of the photovaltaic effect (solar power production process) and then a RLC circuit will be modeled that is powered by a photovaltaic panel.
    tuningfrequency responseLC circuitRLC
    Potential Scenario
    150

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    104

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    2017-Fred_Adler-Mathematically Modeling Asthma
    Our Asthma models have examined how a viral infection can tip the immune system into a different state, with the potential to predispose an individual to future asthma
    infectionasthmaimmune responserhinovirus
    Modeling Scenario
    382

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    472

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    4-060-CircuitTuner-ModelingScenario
    We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to tune a radio to a certain input frequency.
    resistanceciircuittuned mass tunerfrequencyKirchhoffvoltagegainfrequency responseamplitudes Voltage LawinductancecapacitorI am currently working in redesining an existing microbiology course. I would like to be part of ed
    Potential Scenario
    112

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    56

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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus.
    frequencyresonancecoupled oscillator
    Potential Scenario
    124

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    39

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    2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
    Walk through the cases in context of second order linear constant coefficient differential equation with driving function
    driving functionviscousmechanical system
    Potential Scenario
    120

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    61

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    0

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    2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
    A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
    delaytime delystep response
    Potential Scenario
    124

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    70

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    0

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    2019-Fred_Brauer-The_Final_Size_of_a_Serious_Epidemic
    In an epidemic of a serious disease, there is likely to be behavioral response that decreases the epidemic size considerably.
    epidemicfinal sizebehavioral responseSIER modelrelations
    Potential Scenario
    149

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    78

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    2010-Keesom-EtAl-Fishing for Answers Investigating Sustainable Harvesting Ra
    The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be determined to maintain a steady population of Alaskan salmon.
    fisheriesEuler's methodnonlinearlogistic harvestingcanabalismsalmon
    Modeling Scenario
    322

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    211

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    9-012-PDEGuitarTuning-ModelingScenario
    We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.
    extensionsine wavesfrequencyguitardampingFourierstringtuning
    Potential Scenario
    227

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    77

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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates
    Potential Scenario
    149

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    73

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    2016-Roberto_Camporesi-A fresh look at linear ordinary differential equations with constant coefficients
    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator.
    impulseGreen functionsinstructional exposition
    Free Online Textbook
    467

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    98

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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
    spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions
    Modeling Scenario
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    1407

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    5-040-TunedMassDamper-Part-I-Modeling Scenario
    We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.
    structurespring-mass-dashpotspring massearthquakevibrationtuned mass tunerrestoring forcecontroldampe
    Potential Scenario
    135

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    38

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    1992-CHF_Bulte-The differential equation of the deflection curve
    This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint BVP.
    beamdeflectionshear forcebending momentcritical loadnatural frequency
    Modeling Scenario
    260

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    209

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    3-071-WirelessTelegraphy-ModelingScenario
    This project has three parts, (1) done at home, (2) and (3) in class. In (1) we recall how to solve second order differential equations with constant coefficients and simple source functions. In class understand resonance and beats.
    bRLC circuitresonancebeatscurrentwireless telegraphyLC circuit
    Potential Scenario
    141

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    67

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    2017-Allali-EtAl-Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection
    The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies.
    logisticHBV infectionadaptive immunie responseT-lymphocytes