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    Modeling Scenario
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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
    energymass-spring systemkinetic energypotential energytotal energy
    Potential Scenario
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    61

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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
    Modeling Scenario
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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
    climateenergytemperaturelinearizationphase linesenergy balance modelroot finding
    Potential Scenario
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    54

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    2009-James_May-Nonlinear vibration control of long flexible structures
    An automated, non-linear control scheme was developed to transfer energy from the fundamental vibration mode, where most vibration energy of the structures of interest resides, to higher order modes where vibration impedance was shown to be...
    vibrationdampingtuned mass damperviscousnodalmodel dampingflexible structureenergy transfer
    Modeling Scenario
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    294

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    1-050-BargingAhead-ModelingScenario
    As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.
    optimizationkineticsenergytrophic efficiencyworkriverterminal velocityfrictioncurrentforcebargeworlkspeed
    Potential Scenario
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    40

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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
    Modeling Scenario
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    400

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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.
    Association & Data Fittingmassspring-mass systemspring\total distancenumerical differentiation
    Potential Scenario
    127

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    68

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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 bottle dynamics.
    Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem
    Modeling Scenario
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    1-047a-CondensationOptimization-ModelingScenario
    We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
    simulationdataoptimizationenergycondensationbest fitcostsum of scquare errors
    Modeling Scenario
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    115

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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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    29

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    2008-Jai-Li-Differential equations models for interacting wild and transgenic mosquito populations
    We formulate and study continuous-time models, based on systems of ordinary differential equations, for interacting wild and transgenic mosquito populations.
    Mosquito borne diseasespopulationsHolling-II-type mating ratestransgenic mosquitoesnonhyperbolic equilibriummosquitoes
    Potential Scenario
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    62

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    1992-Jude_Sommerfeld-More Applied Math Problems on Vessel Draining
    From a chemical engineering point of view emptying processing and storage tanks is important and this article considers many issues and shapes of containers. The main interest is in the total time it takes to empty the tank for a collection of...
    Torricelli's LawemptyTorricellivesselcontainer
    Potential Scenario
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    49

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    2009-Chellaboina-EtAl-Modeling And Analysis-Mass Action Kinetics
    Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of reactions, that is, reaction networks. These models are a special form of compartmental systems, involving mass- and energy-balance relations.
    dynamical systemschemical reactionreaction networkmass action
    Modeling Scenario
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    1-038-Ebola-ModelingScenario
    Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
    population dynamicsdata analysisexponential growthEbolalogisticepidemic
    Potential Scenario
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    69

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    2009-G_Recktenwald-Tank Draining Exercise
    This paper describe deep mathematics, including differential equations concerned with modeling the draining of tank and the shape of the water coming out the bore hole at the bottom of the tank of water.
    laboratorytankLabViewBermoulli equationempty drainingcolumn of liquidpressure
    Potential Scenario
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    1999-Marchand-McDevitt-Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations
    The project takes full advantage of analytical, numerical, and qualitative techniques to explore the mechanical vibrations of buildings during an earthquake.
    earthquakenondimensionalizationCoulomb dampingmechanical vibration
    Modeling Scenario
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    364

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    3-104-BungeeJumping-ModelingScenario
    In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.
    designfallingmassspring\bungeeelesticityrecommendationconsult
    Modeling Scenario
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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts
    Modeling Scenario
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    3-067-RLCSeriesCircuit-ModelingScenario
    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical...
    resistanceMultisimcircuitRLC circuitinductancecapacitancecimulationgoverning equation
    Modeling Scenario
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    3-092-WirelessPower-ModelingScenario
    We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
    DESMOSwireless power transmissionelectric circuitsKirchhoff's Voltage Law