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    Potential Scenario
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    2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
    Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
    kinematicscurve designhighway exittangential acceleration
    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
    Modeling Scenario
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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
    Modeling Scenario
    310

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    194

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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
    projectile motionaccelerationNewton's Law of Coolingspeeding
    Modeling Scenario
    364

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    362

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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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    169

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    3-009-BallDropInWater-ModelingScenario
    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
    resistancegravityfalling bodyterminal velocitybuoyancy
    Modeling Scenario
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    195

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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
    Potential Scenario
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    2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
    Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.
    falling bodydimensional analysisdrag
    Modeling Scenario
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    3-016-FallingCoffeeFilters-ModelingScenario
    We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.
    resistanceFree Body Diagramcoffee filterforcegraviityfalling object
    Modeling Scenario
    268

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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
    Modeling Scenario
    210

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    235

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    4-036-AltitudeDependentGravity-ModelingScenario
    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
    agravityprojectilelinearizationltitufealtitude
    Modeling Scenario
    214

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    114

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    3-020-ChordPathTime-ModelingScenario
    Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.
    Unit CirclepathfallinggravitychordNetwon's Second Law of Motion
    Modeling Scenario
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    182

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    3-042-CatapultLaunch-ModelingScenario
    We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to give the best lift.
    projectile motioncatapultuphilllaunch angle