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    2017-Varanis-Mereles-Mathematical Model of a Vehicle Crash A Case Study
    The model proposed in this paper allows one to obtain the parameters of the system, and then compare them with the ones obtained experimentally to test the suitability of the model with the vehicle...

    Keywords: case studyRunge-Kuttaspring mass dampervehicle crash

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    2017-Guy-Bart_Stan-Modelling in Biology
    This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.

    Keywords: spring massbifurcationmass actionlimit cycles

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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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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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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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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

    Keywords: Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency

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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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    3-034-CarSuspension-ModelingScenario
    We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'',...

    Keywords: designspring-mass-dashpotspring constantunderdampingcar suspensionsuspension tolerancestatic equilibrium

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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the...

    Keywords: driversteady statesum of square errors

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    3-110-MilitarySpringMassApplication-ModelingScenario
    The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation,...

    Keywords: dampingresonancebeatsspring-mass systemLaplace TransfomDirac Delta function

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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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    Is Earth Currently Undergoing a Sixth Mass Extinction?
    The five Phanerozoic mass extinctions were central in shaping biodiversity on Earth today. Due to increasing biodiversity losses, there is debate about whether we are currently undergoing a sixth...

    Keywords: conservationBiodiversityextinctionMass ExtinctionDeep Time

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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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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.

    Keywords: differential equationsmodelingtextbook

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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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    1-019-RocksInTheHead-Modeling Scenario
    We describe an experiment with data on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. Students use the logistic differential equation as a...

    Keywords: logistic growthparameter estimationexperiment

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    2011-Steven_Desjardins-Remi_Vaillancourt-Ordinary_Differential_Equations_Laplace_Transforms_and_Numerical_Methods_for_Engineers
    This text is packed with worked out presentations, problems, and exercises (with solutions) and MatLab code. There is sufficient detail and attention to topics to more than address interests/needs...

    Keywords: modelingtextbookmatlabengineeringLaplace transform

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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several...

    Keywords: kineticsbiochemical reactionreactantsproducts

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    2018-Yu-Craciun-Mathematical_Analysis_of_Chemical_Reaction_Systems
    These models of chemical reactions are systems of coupled nonlinear differential equations on the positive orthant.

    Keywords: biochemicalkineticsreactionreaction networkmass action

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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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