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    Potential Scenario
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    2017-Ben_Finio-Science Buddies – Linear & Nonlinear Springs Tutorial
    This tutorial provides a basic summary of linear and nonlinear springs and their associated equations for force, stiffness, and potential energy.
    spring massstiffnessspringspotential energyforcenonlinear springlinear spring
    Potential Scenario
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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    spring massoscillationHooke's Lawcoupled springsperiodicforcing functionphase portrait
    Potential Scenario
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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing
    Potential Scenario
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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 crash.
    case studyRunge-Kuttaspring mass dampervehicle crash
    Potential Scenario
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    2018-Dyjuan_Tatro-The_Mathematics_of_Cancer-Fitting_Gompertz_Equation_to_Tumor_Growth
    Fitting the Gompertz Model to long term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor growth as a function of time.
    tumorgrowthGompertzfittingparameter
    Free Online Textbook
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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.
    differential equationsmodelingtextbook
    Potential Scenario
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    2007-Bellomo-De_Angelis-Delitala-Lecture Notes on Mathematical Modelling in Applied Sciences
    The Lectures Notes correspond to the first part of the course devoted to modelling issues to show how the application of models to describe real world phenomena generates mathematical problems to be solved by appropriate mathematical methods.
    spring massLegendre polynomialsintegro-differential equationskinetic theory
    Potential Scenario
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    2018-Joseph-EtAl-A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
    In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population.
    asthmatobacco smokeLiao’s Homotopy analysis Method (environmental pollutants
    Potential Scenario
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    2008-Padir-EtAl-Teaching Differential Equations in a Diverse Classroom
    The interesting portion of this paper are the descriptions of student projects offered: Vibrations of a 3-Story Building in an Earthquake, Triple Pendulum, Nonlinear Circuit. Phase portraits were offered in each case.
    circuitearthquakevibrationpendulumbuikldingtriple pendumlumnonlinear circuit
    Potential Scenario
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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
    goal functionabsolute error curvesinvers methodholling-Tanner model
    Potential Scenario
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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates
    Potential Scenario
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    2011-Nguyen-Shi-Modeling the absorption circulation and metabolism of tirapazamine
    This apparently is a student project and it develops the kinetic model, uses Matlab for numerical solution, analytic solution and numerical solution.
    absorptionMichaelis-MentenMetabolismdrug metabolismcirculation
    Potential Scenario
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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment
    Potential Scenario
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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 of speed.
    spring massjumpjumping
    Potential Scenario
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    2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
    The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
    HangtimeTauberian IdentitiesRoad RunnerWile E. Coyote
    Potential Scenario
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    2013-Boscolo-Stellato-Undergraduate study of harmonic and parametric motion of a simple spring-mass system from motion waveforms
    In this paper, we describe a laboratory exercise that caters to beginning students while giving those with more background an opportunity to explore more complex aspects of the motion.
    laboratoryexperimentspring massair frictionapparatuswaveforms
    Potential Scenario
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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.
    NetLogospring massagent-baseddrapingyarnfabric
    Potential Scenario
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    2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study 
    To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy.
    longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics
    Potential Scenario
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    2017-Biswasa-EtAl-Mathematical Modeling Applied to Sustainable Management of Marine Resources
    We study a nonlinear mathematical model of fishery management to understand dynamics of a fishery resource system in an aquatic environment that consists of two zones; one free fishing zone and another reserve zone where fishing is strictly...
    natural resourcesmarine resourcesfishery model
    Potential Scenario
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    2016-Starling-EtAl-Local Brewery - A Project for Use in Differential Equations Courses
    We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer.
    BEERFermentationbrewery