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  1. 3-016-FallingCoffeeFilters-ModelingScenario

    3-016-FallingCoffeeFilters-ModelingScenario

    2022-05-21 05:10:10 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/H1WK-M188

    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.

  2. 3-017-StackedCoffeeFiltersFalling-ModelingScenario

    3-017-StackedCoffeeFiltersFalling-ModelingScenario

    2022-05-21 03:54:29 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/SQ6S-J782

    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. Parameters need to be estimated and models compared.

  3. 3-019-ShuttleCockFalling-ModelingScenario

    3-019-ShuttleCockFalling-ModelingScenario

    2022-05-21 03:55:19 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/JD09-M668

    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models.

  4. 3-026-SpringInverseProblem-ModelingScenario

    3-026-SpringInverseProblem-ModelingScenario

    2022-05-21 03:56:03 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/3XFZ-RZ66

    We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

  5. 3-027-BobbingDropping-ModelingScenario

    3-027-BobbingDropping-ModelingScenario

    2022-05-21 03:57:03 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/EZGZ-5T49

    We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.

  6. 3-029-FerrisWheelCatch-ModelingScenario

    3-029-FerrisWheelCatch-ModelingScenario

    2022-05-21 03:57:47 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/EQV9-YA59

    We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.

  7. 3-030-SecondOrderIntro-ModelingScenario

    3-030-SecondOrderIntro-ModelingScenario

    2022-05-21 03:58:33 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/Y8S9-C814

    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 modeling activities.

  8. 3-031-SpringCost-ModelingScenario

    3-031-SpringCost-ModelingScenario

    2022-05-20 22:13:00 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/N71R-J453

    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 cost.

  9. 3-035-StadiumDesign-ModelingScenario

    3-035-StadiumDesign-ModelingScenario

    2022-05-20 22:13:51 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/MTN0-RV51

    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?

  10. Machine Learning Meets Medicine with Jenessa Peterson

    Machine Learning Meets Medicine with Jenessa Peterson

    2022-05-20 21:04:11 | Teaching Materials | Contributor(s): Janessa Peterson, Megan Seifert | doi:10.25334/Y907-Y370

    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 web-based voter data tracking platform, anomaly detection models for skin lesions and eye disease, and a...

  11. 3-040-FirstPassageTime-ModelingScenario

    3-040-FirstPassageTime-ModelingScenario

    2022-05-20 22:14:45 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/XNS7-ST57

    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.

  12. Climate Change Module (Project EDDIE) for Introductory Statistics

    Climate Change Module (Project EDDIE) for Introductory Statistics

    2022-05-20 20:25:53 | Teaching Materials | Contributor(s): Jessie Oehrlein | doi:10.25334/KKGD-AP27

    Students practice and deepen their understanding of bivariate numerical data analysis (correlation, linear regression, etc.) through working with data related to climate change. Adapted from a module produced by Project EDDIE.

  13. 3-041-UpDown-ModelingScenario

    3-041-UpDown-ModelingScenario

    2022-05-20 22:15:41 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/8XY8-C736

    Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.

  14. 3-042-CatapultLaunch-ModelingScenario

    3-042-CatapultLaunch-ModelingScenario

    2022-05-20 17:27:20 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/JRPS-5H67

    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 give the best lift.

  15. 3-050-CometOrbitalMechanics-ModelingScenario

    3-050-CometOrbitalMechanics-ModelingScenario

    2022-05-20 17:28:03 | Teaching Materials | Contributor(s): Johan Thiel | doi:10.25334/SFQJ-8737

    The broad goal of this activity is to use a basic numerical method to approximate the solution of an initial value problem. In this particular case, we will use Euler's method to help model the trajectory of a comet as it orbits the sun.

  16. 3-054-Relay-ModelingScenario

    3-054-Relay-ModelingScenario

    2022-05-20 16:28:16 | Teaching Materials | Contributor(s): Brian Winkel | doi:10.25334/TMFG-Y761

    We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.

  17. 3-055-FloatingBox-ModelingScenario

    3-055-FloatingBox-ModelingScenario

    2022-05-20 16:29:24 | Teaching Materials | Contributor(s): John Thoo | doi:10.25334/ZTTA-6188

    In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.

  18. 3-060-DataToDifferentialEquation-ModelingScenario

    3-060-DataToDifferentialEquation-ModelingScenario

    2022-05-20 14:25:58 | Teaching Materials | Contributor(s): Eric Sullivan, Kelly Cline | doi:10.25334/119D-2408

    Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.

  19. 3-064-GearTrain-ModelingScenario

    3-064-GearTrain-ModelingScenario

    2022-05-20 14:26:43 | Teaching Materials | Contributor(s): Lukasz Grabarek | doi:10.25334/06KW-W970

    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 moments of inertia of the gear train components.

  20. 3-067-RLCSeriesCircuit-ModelingScenario

    3-067-RLCSeriesCircuit-ModelingScenario

    2022-05-20 14:27:33 | Teaching Materials | Contributor(s): Virgil Ganescu | doi:10.25334/43M0-7X98

    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 the data acquired from analyzing the numerical model.