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    Potential Scenario
    183

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    1994-Roland_Minton-A Progression of Projectiles-Examples from Sports
    There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,
    sportsresistanceprojectilebaseballdraglinear resistancequadratic resistancetennis
    Modeling Scenario
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    3-051-ProjectileMotions-ModelingScenario
    We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
    trajectorylaunching radiantprojectile motionprojectileno resistanceangle of launch
    Modeling Scenario
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    712

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    3-043-BallisticModeling-SpongeDart-ModelingScenario
    The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.
    projectile motionair resistanceballisticsdimensional analysisNewtonian mechanicssponge dartNerf gunNerf dartBuckingham's Theorem
    Modeling Scenario
    377

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    291

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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
    Potential Scenario
    139

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    50

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    2014-Groetsch-Yost-Vertical Projection in a Resisting Medium - Revelations on Observations of Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
    resistanceprojectile
    Modeling Scenario
    264

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    321

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    1-077-RLMSimSeriesCircuit-ModelingScenario
    In this validation setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using...
    MeasurementcircuitvoltagecurrentvalidationSPICERL circuitMultilsim
    Modeling Scenario
    291

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    288

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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?
    projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance
    Article or Presentation
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    48

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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
    resistanceprojectile motionprojectilefluidMersenne
    Modeling Scenario
    203

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    234

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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
    783

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    362

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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
    resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket
    Modeling Scenario
    326

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    381

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    5-040-TunedMassDampers-PartII-ModelingScenario
    Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...
    structureresistancespring-mass-dashpotearthquakevibrationcontroldampingtuned mass damperstiffnessreduction of vibration
    Modeling Scenario
    215

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    209

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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.
    Spring 2020 workshopvibrationtuningdriverresonanceforced vibrationundampedbeatsnaturl frequency
    Modeling Scenario
    249

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    369

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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
    Article or Presentation
    160

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    56

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    1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom
    The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick.
    differential equationsresistancegravityfree fallaccelerationballoon
    Potential Scenario
    132

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    40

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    2002-Chai-Optimal initial angle to fire a projectile
    Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance traveled by the projectile?”
    optimizationprojectile motionlaunch angle
    Potential Scenario
    139

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    49

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    2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study
    We develop an epidemiological model that can be used to address the spread of resistance at the population level, and a virus dynamics model that can be used to study the dynamics of virus over the time course of an individual’s infection.
    stabilityresistancevirusdrugepidemic competitionimmune responserhinovirus
    Potential Scenario
    166

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    59

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    2017-CW_Groetsch-Hammer and Feather - Some Calculus of Mass and Fall Time
    Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a falcon feather on the surface of the moon to give a dramatic illustration that this is not so.
    gravityfree falllinear resistancequadratic resistancehammerfeatherMoon resistanceGalileo
    Modeling Scenario
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    3-095-ShotInWater-ModelingScenario
    This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.
    projectile motionterminal velocityprojectilewater resistancereduction of orderfrictionair resistance
    Potential Scenario
    130

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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
    Free Online Textbook
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    78

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    2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology
    I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.
    biologytextbooksystemsdyanmical system