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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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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?

    Keywords: projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance

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    Machine Learning Meets Medicine with Jenessa Peterson
    Jenessa Peterson is a former teacher turned data scientist/engineer and Director of Learning Engineering at The Learning Agency. Her more recent work in data science has included building a...

    Keywords: data sciencemachine learningmedicine

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    3-042-CatapultLaunch-ModelingScenario
    We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to...

    Keywords: projectile motioncatapultuphilllaunch angle

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    3-064-GearTrain-ModelingScenario
    Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and...

    Keywords: frictiongearspur geargear traintorquegear ratioangular accelerationangular velocitymoment of inertiadouble reduction gear

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    3-067-RLCSeriesCircuit-ModelingScenario
    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with...

    Keywords: resistanceMultisimcircuitRLC circuitinductancecapacitancecimulationgoverning equation

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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...

    Keywords: bRLC circuitresonancebeatscurrentwireless telegraphyLC circuit

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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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    3-073-EarthQuakePartII-ModelingScenario
    Your goal here is to determine how much friction/damping should be designed into a building to keep the roof from moving too far (which would result in the entire building collapsing) when it...

    Keywords: earthquakevibrationdampingamplitudespring-mass systemsteady-state solutionunderdamped

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    3-076-CircuitBuilding-ModelingScenario
    In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.

    Keywords: simulationexperimentMultisimcircuitinductancecapacitorKirchhoff's Voltage Lawresistor

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    3-075-RLCCircuits-ModelingScenario
    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

    Keywords: resistancecircuitvoltageinductancecapacitancecurrentKirchhoff's Law

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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is...

    Keywords: DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law

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    3-101-SpringMassFirstTry-NoResistance-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.

    Keywords: frequencymassoscillationundampedspring constantspring\Single Degree of Freedom System

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    3-102-SpringMassDamped-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.

    Keywords: frequencymassoscillationstiffnessspring constantspring\dampedSingle Degree of Freedom Systemcoefficient

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    4-020-AnIEDBlast-ModelingScenario
    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use...

    Keywords: applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces

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    4-065-GasInjection-ModelingScenario
    Students use programs (or create their own code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest...

    Keywords: Prandtl-Blasius equationsboundary layergas injectionesponential box schemeuniform convergenceFORTRAN

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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF)...

    Keywords: vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension

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    5-040-TunedMassDampers-PartII-ModelingScenario
    Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a...

    Keywords: structureresistancespring-mass-dashpotearthquakevibrationcontroldampingtuned mass damperstiffnessreduction of vibration

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    5-080-SpaceFlightRecolonize-ModelingScenario
    This project is a combination of differential equations, multi-variable calculus, and vector calculus with use of technology to model colonization of a new planet. Students solve a system of...

    Keywords: optimizationsum of square errorsvector calculusLagrange multipliersline integrals

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    5-090-SolidParticleErosion-ModelingScenario
    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges...

    Keywords: classical mechanicssolid mechanicsNewton's Laws of Motionrigid bodyplasticitypittingductile surface

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