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    Potential Scenario
    156

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    48

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    2009-Reid-King-Pendulum Motion and Differential Equations
    This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior.
    pendulumphysical pendulum
    Potential Scenario
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    2002-Fay-The Pendulum Equation
    We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it.
    pendulumFourier seriesTaylor seriesnumerical solution
    Modeling Scenario
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    3-085-SimplePendulum-ModelingScenario
    Thestudent is asked to derive and solve a differential equation that gives the position (angle
    Newton's Second Law of Motionpendulumkinetic energypotential energyConservation of Energytinitial conditionssmall angle approximationTaylor polynomialpercent error
    Potential Scenario
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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
    pendulumLotka Volterra equationsexistenceuniqueness
    Potential Scenario
    187

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    64

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    2006-Salem-Abudiab-Labview-An Interactive Teaching Tool for a Differential Equations Class
    It is evident that computer based learning has become an essential part of education systems. It provides animation and interactive processes that are not possible with textbooks.
    javavisualizationvirtual labpendulumLabviecomputer assisted instructionharmonic motion
    Modeling Scenario
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    301

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    6-002-EulerCromerPendulum-ModelingScenario
    This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
    pendulumsemi-implicit methodsEuler-Cromernumerical solvers
    Modeling Scenario
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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
    gravityinverse problemacceleration
    Modeling Scenario
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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
    Free Online Textbook
    216

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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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    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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    48

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    1987-MS_Greenwood-Using videotapes to study underdamped motion of a pendulum
    Using a video camera to study the effects of air resistance acting on pendulum bob, ping-pong ball, styrofoam spheres, and brass spheres.
    Videoresistancependulumping-pong ballstyrofoam ballbrass ball
    Potential Scenario
    111

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    62

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    2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
    This article describes an equation of motion for a waggling pendulum.
    resonanceinverted pendulummechanicsdamped pendulum
    Free Online Textbook
    127

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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.
    orbitstwo mass systematommagnetic fieldcoupled penduluminverted pendulumcharged particleKepler motion
    Potential Scenario
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    2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
    In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in classical mechanics.
    population dynamicsecologydynamicsclassical mechanicschemical reaction
    Potential Scenario
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    2009-Peter-Howard-Modeling With ODE
    This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.
    ratescompetitionpopulationepidemicpendulumcarbon datingreaction chemistrymechanicsplanetary motiondrag racingHamilton’s methodvariational method
    Potential Scenario
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    2018-Kovacs-Insperger-Retarded neutral and advanced differential equation models for balancing using an accelerometer
    It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models.
    feedbackAccelerometersfunctional differential equationssemi-discretizationD-subdivision method
    Free Online Textbook
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    2015-Dan_Sloughte-Notes on Diffy Qs Differential Equations for Engineers
    This is a calculus book with the last chapter devoted to ordinary differential equations topics. The effort begins with a study of numerical methods and goes through traditional technique strategies.
    Numerical Methodspendulumtext
    Modeling Scenario
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    1-107-ClothDry-ModelingScenario
    We build a mathematical model for the rate of drying in a wet cloth while hanging in air. A model can be based on underlying physical principles (analytic) or based on observations and reasoned equations, but no physical assumptions (empirical).
    dryingclothevaporation
    Potential Scenario
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    2018-W_Hohenauer-Physical modelling based on first order ODEs
    An introduction in techniques to solve first order ODE´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth effects are discussed.
    dischargecapacitormagnetic fieldinductionmagnetic induction
    Modeling Scenario
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    9-020-HeatDiffusion-ModelingScenario
    This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
    laboratoryDiffusionheat