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Modeling Scenario
609
views
815
downloads
0
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3-002-ModelsMotivatingSecondOrder-ModelingScenario
Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.
resistance
spring mass
oscillation
Hooke's Law
dampening
Modeling Scenario
335
views
149
downloads
0
comments
1-105-AnimalFall-ModelingScenario
This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall
Modeling Scenario
391
views
265
downloads
0
comments
5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws
sensitivity analysisanalysis
Modeling Scenario
203
views
211
downloads
0
comments
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 motion
terminal velocity
projectile
water resistance
reduction of order
friction
air resistance
Modeling Scenario
392
views
594
downloads
0
comments
1-076-ClimateBifurcation-ModelingScenario
We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
energy balance
climate
energy
albedo
Hysteresis
bifurcation
ice-age
greenhouse
balance
Stefan Boltzmann Law
Modeling Scenario
340
views
448
downloads
0
comments
1-028-SouthernSweetIcedTea-ModelingScenario
We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea should steep before essentially reaching saturation.
data
Newton's Law of Cooling
tea
sweet tea
Modeling Scenario
235
views
504
downloads
0
comments
3-076-CircuitBuilding-ModelingScenario
In this project students will establish a mathematical model for an electric circuit as a second-order ordinary differential equation with constant coefficients.
simulation
experiment
Multisim
circuit
inductance
capacitor
Kirchhoff's Voltage Law
resistor
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