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    Modeling Scenario
    249

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    117

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    0

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    3-041-UpDown-ModelingScenario
    Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.
    gravityprojectile motionfalling bodymaximum heightftiming
    Potential Scenario
    131

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    67

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    1999-F_Brauer-What Goes Up Must Come Down
    This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces.
    projectilefrictionfalling timerising timemaximum height
    Article or Presentation
    131

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    47

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    0

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    1999-F_Brauer-What_Goes_Up_Must_Come_Down
    It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces that are nonlinear functions of velocity.
    resistancefallingprojectilevertical projectile
    Modeling Scenario
    1093

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    179

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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
    Potential Scenario
    147

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    56

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    2008-Ratneesh_Suri-Optimal harvesting strategies for fisheries-differential equations approach
    We develop and investigate the harvesting model in both deterministic and stochastic settings. We first employ the Expected Net Present Value approach and determine optimal harvesting policy using various optimization techniques including optimal...
    optimal controlsustainable yieldmaximum sustainable yieldharvestExpected Net Present Valuecalculus of variationsdynamic programmingmaximum economic yield
    Potential Scenario
    186

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    84

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    0

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    2017-Gilbert-Lewis-Harvesting of renewable natural resource
    This is a resource to accompany a commercial text book and has a tutorial nature with some analysis and several good exercises
    logisticmaximum sustainable yieldwhaleharvestrenewable resourceconstant harvest
    Article or Presentation
    164

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    30

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    0

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    2013-Brian_Winkel-An_Optimal_Control_Model_in_Insect_Colonies
    we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at the end of a season.
    insect colonyoptimal controlparameter
    Modeling Scenario
    305

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    207

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    0

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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...
    compartmentsalttankmixingflow
    Modeling Scenario
    355

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    207

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    5-022-ColdPill-ModelingScenario
    A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation model, use known parameter values, and plot solutions.
    ratesmedicinedrug discoverycompartmentcold pillgastrointestinalbloodstream
    Modeling Scenario
    266

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    253

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    0

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    1-052-SaltWaterTanks-ModelingScenario
    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.
    salttankmixing
    Potential Scenario
    249

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    40

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    0

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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium
    Modeling Scenario
    260

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    210

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    0

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    3-105-FrequencyResponse-ModelingScenario
    We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
    transient dynamicscircuitspring massdriverfrequency responseamplitudesteady state
    Potential Scenario
    133

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    73

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    2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
    In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.
    Accelerometersfree falljumptrampoline
    Modeling Scenario
    365

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    589

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    3-103-PullBackCars-ModelingScenario
    This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
    modelingdynamicshands-ontoypull-back carpullback
    Modeling Scenario
    280

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    149

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    0

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    3-063-FallingBuildingIce-ModelingScenario
    We model the fall of a piece of ice which is falling from a high building in New York City.
    resistancefallinggravityiceterminal velocityskyscrapers
    Modeling Scenario
    473

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    280

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    0

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    1-145-FastPitch-ModelingScenario
    We consider the problem of comparing pitch velocities using measurement methods in different eras of baseball.
    Measurementresistanceair resistancebaseballpitcherfast
    Modeling Scenario
    308

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    282

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    1-127-FishHarvesting-ModelingScenario
    We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not necessarily mathematicians).
    Management Of Dataoptimal controlfisherieslogisticharvestingmaximum sustainable yield
    Modeling Scenario
    332

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    459

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    3-099-PullBack-ModelingScenario
    We guide students through the development of an empirical model for the velocity and distance traveled of a simple pull-back toy. Students can record videos and extract data using their own pull-back toy or use data included.
    dynamicspull-back toy
    Modeling Scenario
    477

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    246

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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
    optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable
    Potential Scenario
    146

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    40

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor