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Downloads
Views
Date
Relevance
Modeling Scenario
223
views
109
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Modeling Scenario
206
views
218
downloads
0
comments
3-069-HeatInBar-ModelingScenario
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
heat transfer
experiment
conduction
convection
boundary conditions
finite volume method
Modeling Scenario
243
views
215
downloads
0
comments
1-054-GrowthInFarmland-ModelingScenario
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...
fitting
farm
farmland
Modeling Scenario
549
views
311
downloads
0
comments
6-020-AlgaePopulationSelf-Replenishment-ModelingScenario
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A
algae
population
Mexico
qualitative
compartment
linearization
Jacobian
lak
nondimensionalization
pplane
Potential Scenario
201
views
46
downloads
0
comments
2010-Shaza_Hussein-Predator-Prey Modeling
The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible.
population dynamics
predator-prey
logistic equation
Endangered Cats
decreasing population
rabbits
foxes
Potential Scenario
131
views
77
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
mass
oscillation
spring\
coupled springs
periodic
fporcing
Potential Scenario
126
views
69
downloads
0
comments
2002-Fay-The Pendulum Equation
We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it.
pendulum
Fourier series
Taylor series
numerical solution
Modeling Scenario
240
views
376
downloads
0
comments
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 Fitting
mass
spring-mass system
spring\
total distance
numerical differentiation
Modeling Scenario
223
views
473
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
Potential Scenario
123
views
48
downloads
0
comments
2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
phytoplankton
bifurcation
orbits
herbivorous zooplankton
effect of fish
maturation time delay
Technique Narrative
859
views
115
downloads
0
comments
3-090-ChebyshevPolynomialSolution-TechniqueNarrative
The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
series soluotion
polynomial solutions
Chebyshev polynomials
Chebyshev differential equations
Modeling Scenario
233
views
178
downloads
0
comments
1-083-FallingMeteorites-ModelingScenario
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...
falling object
drag
variable mass
factor ranking
meteor
meteorite
Modeling Scenario
219
views
413
downloads
0
comments
9-020-HeatDiffusion-ModelingScenario
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
laboratory
Diffusion
heat
Potential Scenario
104
views
35
downloads
0
comments
2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
ice
ice spike
bulk heat transfer
mass conservation
Modeling Scenario
265
views
165
downloads
0
comments
1-136-MarriageAge-ModelingScenario
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these...
messages
marriage
using social sciences in forecasting
directed
Modeling Scenario
695
views
674
downloads
0
comments
3-034-CarSuspension-ModelingScenario
We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
design
spring-mass-dashpot
spring constant
underdamping
car suspension
suspension tolerance
static equilibrium
Modeling Scenario
333
views
1168
downloads
0
comments
6-025-WhalesAndKrill-ModelingScenario
Students will use Excel to observe qualitative behavior in a simulation of a predator-prey model, with blue whales and krill as the predator and prey populations, respectively.
krill
whale
predatpr-prey
Modeling Scenario
238
views
153
downloads
0
comments
5-025-SaltCompartments-ModelingScenario
Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
compartment
salt
tanks
Potential Scenario
143
views
64
downloads
0
comments
1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.
prediction
forest fire
fire management
fire spread
fuel
Potential Scenario
123
views
40
downloads
0
comments
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?”
optimization
projectile motion
launch angle
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