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    Modeling Scenario
    989

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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 modeling activities.
    parameter estimationnon-homogeneousSpanishfrequencybuoyancyinverse problemthrustunderdampedfirst passagespring mash dashpotrealcomplexhomogeneoussuperpositionparachuteoverdampedcritically dampedbuoyquadratic equationrootsrocket flight
    Potential Scenario
    130

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    66

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    1999-F_Brauer-What Goes Up Must Come Down
    This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces.
    projectilefrictionfalling timerising timemaximum height
    Modeling Scenario
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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 the model to determine the results of a dynamical...
    applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces
    Modeling Scenario
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    369

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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 under power and then without power followed by its...
    resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket
    Modeling Scenario
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    157

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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.
    frequencymassoscillationstiffnessspring constantspring\dampedSingle Degree of Freedom Systemcoefficient
    Modeling Scenario
    258

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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
    Potential Scenario
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    38

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    1992-CHF_Bulte-The differential equation of the deflection curve
    This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint BVP.
    beamdeflectionshear forcebending momentcritical loadnatural frequency
    Potential Scenario
    158

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    51

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    2018-Winkle-Igoshin-Bennett-Josic-Ott-Modeling_Mechanical_Interactions_in_Growing_Populations_of_Rod-Shaped_Bacteria
    Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions.
    bacteriaagent-basedpopulationbrod-shapedcellular growth
    Modeling Scenario
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    1-004-MicroorganismImmigration-ModelingScenario
    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.
    continuousimmigrationpopulationdeathdiscrete
    Potential Scenario
    133

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    73

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    2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
    In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.
    Accelerometersfree falljumptrampoline
    Modeling Scenario
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    393

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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 spring-mass-dashpot with stiffness replacing spring...
    structureresistancespring-mass-dashpotearthquakevibrationcontroldampingtuned mass damperstiffnessreduction of vibration
    Modeling Scenario
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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 structure as a spring-mass-dashpot system.
    structurespring-mass-dashpotspring massearthquakevibrationtuned mass tunerrestoring forcecontroldampe