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    Modeling Scenario
    250

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    499

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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.
    phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation
    Potential Scenario
    361

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    62

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    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
    dynamical systemsregulationsteady statesales modelexternal stimulus
    Modeling Scenario
    217

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    303

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    5-015-RunnersSynchronize-ModelingScenario
    In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena.
    predatorAutonomous equationsoscillationcoupled oscillatorsynchronyrunnerpreyKuramato model
    Modeling Scenario
    225

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    214

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
    Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency
    Potential Scenario
    170

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    41

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    1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data
    With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations.
    circuitTorricelli's LawHooke's LawRC circuitharmonic oscillatorglucoseglucose tolerance test
    Potential Scenario
    201

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    54

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    2009-Shamim-EtAl-Investigating viscous damping using a webcam
    We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped, critically damped and underdamped regimes of harmonic motion.
    laboratoryunderdampedoverdampedcritically dampedharmonic motionimage processingviscous fluid
    Modeling Scenario
    212

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    228

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    6-075-LorenzSystemSimulation-ModelingScenario
    The Lorenz system is examined by students as a simple model of chaotic behavior or strange attractor. MATLAB code is created to find the numerical solutions of the Lorenz’ system of nonlinear ordinary differential equations using various parameters.
    chaososcillatorLorenzwaterwheelstrange attractorbifurcation effect
    Modeling Scenario
    243

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    123

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    3-040-FirstPassageTime-ModelingScenario
    We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
    oscillatordampedunderdampedfirst passagefirst passage timespring mash dashpot