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    1989-R_Blickhan-Spring Mass Model For Running-Hopping
    A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function...

    Keywords: spring massjumpjumping

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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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    3-002-ModelsMotivatingSecondOrder-ModelingScenario
    Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because...

    Keywords: resistancespring massoscillationHooke's Lawdampening

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    2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts
    We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.

    Keywords: moduleoptimizationspring massmassspring\costTeaching Moduleminimal cost

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    3-091-SpringModeling-ModelingScenario
    In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.

    Keywords: datalaboratoryLoggerProVerniermass-spring systemmodel validationempirical modeltheoretical model

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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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    Synapse Transmission and Action Potentials
    This module introduces action potentials in the context of understanding nerve impulses. It is intended for an introductory biology audience.

    Keywords: InequalitiesOpenStaxAnimal Physiology

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    Electrical Activity of Neurons
    This tutorial describes how neurons generate action potentials, and how scientists measure neuronal activity and record the firing of individual neurons.

    Keywords: Resources @ HHMI - BioInteractiveAnatomy & PhysiologyNervous systemCell communication

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    2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers
    We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the...

    Keywords: vibrationresonancetuned mass damperpeak frequency responseexcitation

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    2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
    We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.

    Keywords: projectstechnical writinginterdisciplinary skills

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    2012-Rusinko-Swan-Agent-Based Fabric Modeling Using Differential Equations
    We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system.

    Keywords: NetLogospring massagent-baseddrapingyarnfabric

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    3-060-DataToDifferentialEquation-ModelingScenario
    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.

    Keywords: Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation

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    3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.

    Keywords: massundampedFree Body Diagramspringstwo springsoscillationspring constantfixed ends

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    5-040-TunedMassDamper-Part-I-Modeling Scenario
    We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original...

    Keywords: structurespring-mass-dashpotspring massearthquakevibrationtuned mass tunerrestoring forcecontroldampe

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    A Momentum-First Approach to Newton’s Second Law
    Students frequently struggle with seeing the connection between forces and motion in introductory physics. This lesson is part of a combined momentum and kinematics unit that first teaches...

    Keywords: group workMomentumNewton's Laws

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    1-012-Sublimation-Modeling Scenario
    We offer data on the sublimation of dry ice (carbon dioxide) collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a...

    Keywords: sublimationdry ice

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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.

    Keywords: spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions

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    1991-Carmine_Chicone-Ordinary Differential Equations with Applications
    This is a complete text for a graduate level course. Hence there is much theory, but there is a chapter on applications with some sophisticated approaches and high level modeling of motion.

    Keywords: orbitstwo mass systematommagnetic fieldcoupled penduluminverted pendulumcharged particleKepler motion

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    3-009-BallDropInWater-ModelingScenario
    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal...

    Keywords: resistancegravityfalling bodyterminal velocitybuoyancy

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    3-026-SpringInverseProblem-ModelingScenario
    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.

    Keywords: datamassinverse problemspring\parameter estimate

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