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    3-072-EarthQuakePartI-ModelingScenario
    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.

    Keywords: earthquakevibrationamplituderesonanceundampedspring-mass system

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    How Do Certain Factors Impact People's Actions Toward Climate Change?
    A survey was conducted to research how age and knowledge about climate change can impact people’s actions regarding it. People have a large impact on the environment so knowing how different groups...

    Keywords: climate change

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    2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
    The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest...

    Keywords: Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem

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    3-030-SecondOrderIntro-ModelingScenario
    We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and...

    Keywords: parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight

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    1986-Istvan_Gyori-Connections between compartment systems pipes and integro-differential equations
    In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given...

    Keywords: physiologypipelinecompartmentbloodcirculationintegro-differential equation

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    3-016-FallingCoffeeFilters-ModelingScenario
    We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.

    Keywords: resistanceFree Body Diagramcoffee filterforcegraviityfalling object

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    3-017-StackedCoffeeFiltersFalling-ModelingScenario
    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power....

    Keywords: dataresistancefalling bodycoffee filterstacked

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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...

    Keywords: oscillatordampedunderdampedfirst passagefirst passage timespring mash dashpot

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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.

    Keywords: transient dynamicscircuitspring massdriverfrequency responseamplitudesteady state

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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...

    Keywords: Unit CirclepathfallinggravitychordNetwon's Second Law of Motion

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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...

    Keywords: dryingclothevaporation

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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight...

    Keywords: resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket

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    Science Behind the Lesson: It's a Bird! It's a Plane! It's Biomechanics!
    Active flight is a specialized mode of movement found in insects, birds, and mammals. The anatomy, morphology, physiology, and ecology of flying taxa has changed over evolutionary time. Researchers...

    Keywords: EvolutionecologybatphysiologyAnatomybiomechanicsbirdFlightinsect

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    Evaluating the Quick Fix: Weight Loss Drugs and Cellular Respiration
    One key to student success in introductory and cell biology courses is a foundational knowledge of cellular respiration. This is a content area in which students often harbor misconceptions that...

    Keywords: data analysisCellular RespirationElectron Transport ChainEnergy transformationsMitochondriaOxidative phosphorylationWeight loss drugs24-dinitrophenol (DNP)

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    Taking the Hassle out of Hasselbalch
    Mention pH in a classroom and you can almost see the inner yawn on the faces of your students. The definition may even roll easily from their lips. However, despite multiple exposures to the...

    Keywords: pHdrug uptakeHenderson-Hasslbalch equationmedical applicationspKa

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    3-095-ShotInWater-ModelingScenario
    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.

    Keywords: projectile motionterminal velocityprojectilewater resistancereduction of orderfrictionair resistance

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    Cookbook for R
    The goal of the cookbook is to provide solutions to common tasks and problems in analyzing data.

    Keywords: Rdata analysisdata manipulationdata

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    2016-Pennell-Avitabile-White-Engineering Applications Differential Equations
    General discussion of an engineering based differential equations course with examples from RC Circuit, mass spring dashpot.

    Keywords: circuitvoltagecapacitornondimensionalization

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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.

    Keywords: laboratoryunderdampedoverdampedcritically dampedharmonic motionimage processingviscous fluid

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    3-031-SpringCost-ModelingScenario
    We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and...

    Keywords: designunit costspring constantstatic equilibriumspring masss dashpot

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