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    Modeling Scenario
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    3-080-PendulumModeling-ModelingScenario
    We lead students through building model for several pendulum configurations in motion and ask students to compare results.
    pendulumperiodlinearization
    Modeling Scenario
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    9-005-InvasiveSpeciesModel-ModelingScenario
    This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion.
    Invasive Specieslogisticmigrationtraveling wavesdispersion
    Modeling Scenario
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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
    Modeling Scenario
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    3-070-FallingInWater-ModelingScenario
    We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters.
    datawaterresistancefallingbuoyancymass
    Modeling Scenario
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    3-063-FallingBuildingIce-ModelingScenario
    We model the fall of a piece of ice which is falling from a high building in New York City.
    resistancefallinggravityiceterminal velocityskyscrapers
    Modeling Scenario
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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.
    projectile motioninclined rampcoefficient of restitutionoptimal anglebounce
    Modeling Scenario
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    3-044-DeepWell-ModelingScenario
    We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.
    gravityprojectile motionfalling bodyspeed of sound
    Modeling Scenario
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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example.
    diseasecommon coldresidence hall
    Modeling Scenario
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    3-020-ChordPathTime-ModelingScenario
    Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.
    Unit CirclepathfallinggravitychordNetwon's Second Law of Motion
    Modeling Scenario
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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
    Modeling Scenario
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    1-107-ClothDry-ModelingScenario
    We build a mathematical model for the rate of drying in a wet cloth while hanging in air. A model can be based on underlying physical principles (analytic) or based on observations and reasoned equations, but no physical assumptions (empirical).
    dryingclothevaporation
    Modeling Scenario
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    6-017-OncolyticViruses-ModelingScenario
    Students explore oncolytic virotherapy using systems of differential equations and numerical simulations.
    cancercancer-immune dynamicsimmune suppressor drugoncolytic virusvirotherapy
    Modeling Scenario
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    10-001-TilingHallway-ModelingScenario
    Students investigate difference equations through tiling hallways. They observe patterns in the tiling which lead to a difference equation. Solutions will be calculated by iteration. and the shift operator.
    Geometryiterationtilingrecurrenceshift operatorpatternsclosed formanalytic solution
    Modeling Scenario
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    1-053-SlimeSpread-ModelingScenario
    We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.
    spreadsheetsslime
    Modeling Scenario
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    1-018-LogisticPopModel-ModelingScenario
    We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic model in these...
    data analysisparameter estimationlogisticCiliate protozoapopulationlimited growthparameciaGause
    Modeling Scenario
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    6-008-PursuitModels-Modeling Scenario
    Students are prompted to build systems of nonlinear differential equations to model pursuit-evader activities in which a pursuer attempts to follow, perhaps track down and come close to, an evader without knowledge of the evader's intentions, just...