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Downloads
Views
Date
Relevance
Modeling Scenario
199
views
157
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
Modeling Scenario
198
views
245
downloads
0
comments
1-114-EarthClimate-ModelingScenario
In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
climate
energy
temperature
linearization
phase lines
energy balance model
root finding
Potential Scenario
111
views
37
downloads
0
comments
2009-James_May-Nonlinear vibration control of long flexible structures
An automated, non-linear control scheme was developed to transfer energy from the fundamental vibration mode, where most vibration energy of the structures of interest resides, to higher order modes where vibration impedance was shown to be...
vibration
damping
tuned mass damper
viscous
nodal
model damping
flexible structure
energy transfer
Modeling Scenario
417
views
253
downloads
0
comments
1-050-BargingAhead-ModelingScenario
As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.
optimization
kinetics
energy
trophic efficiency
work
river
terminal velocity
friction
current
force
barge
worlk
speed
Potential Scenario
92
views
33
downloads
0
comments
2017-Ben_Finio-Science Buddies – Linear & Nonlinear Springs Tutorial
This tutorial provides a basic summary of linear and nonlinear springs and their associated equations for force, stiffness, and potential energy.
spring mass
stiffness
springs
potential energy
force
nonlinear spring
linear spring
Potential Scenario
125
views
47
downloads
0
comments
2013-Kose-Kunze-Climate Modeling in the Calculus and Differential Equations Classroom
We introduce here the basic principles of climate science for a one-dimensional Energy Balance Model (EBM),
climate change
Energy Balance Models
ice albedo
Potential Scenario
91
views
28
downloads
0
comments
2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
Torricelli's Law
Conservation of Energyt
Conservation of Mass
Bernoulli’s Theorem
Potential Scenario
245
views
31
downloads
0
comments
2008-Claire_Vailance-Reaction_Kinetics-Course_Notes
This is but one of several set of notes which may interest the reader on chemical kinetics.
kinetics
parameters
rate constant
chemical kinetics
reactions
Modeling Scenario
277
views
509
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
326
views
283
downloads
0
comments
1-047a-CondensationOptimization-ModelingScenario
We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
simulation
data
optimization
energy
condensation
best fit
cost
sum of scquare errors
Modeling Scenario
298
views
165
downloads
0
comments
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.
optimization
Optimal Control Theory
insect colony
optimal control
natural resources
Pointryagin's Maximum Principle
control variable
Modeling Scenario
159
views
304
downloads
0
comments
3-073-EarthQuakePartII-ModelingScenario
Your goal here is to determine how much friction/damping should be designed into a building to keep the roof from moving too far (which would result in the entire building collapsing) when it undergoes minor vibrations from a small earthquake.
earthquake
vibration
damping
amplitude
spring-mass system
steady-state solution
underdamped
Modeling Scenario
154
views
81
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
Potential Scenario
137
views
37
downloads
0
comments
2009-Chellaboina-EtAl-Modeling And Analysis-Mass Action Kinetics
Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of reactions, that is, reaction networks. These models are a special form of compartmental systems, involving mass- and energy-balance relations.
dynamical systems
chemical reaction
reaction network
mass action
Potential Scenario
114
views
50
downloads
0
comments
1989-R_Blickhan-Spring Mass Model For Running-Hopping
A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.
spring mass
jump
jumping
Article or Presentation
95
views
38
downloads
0
comments
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.
resistance
projectile motion
projectile
fluid
Mersenne
Potential Scenario
113
views
42
downloads
0
comments
2009-G_Recktenwald-Tank Draining Exercise
This paper describe deep mathematics, including differential equations concerned with modeling the draining of tank and the shape of the water coming out the bore hole at the bottom of the tank of water.
laboratory
tank
LabView
Bermoulli equation
empty draining
column of liquid
pressure
Potential Scenario
104
views
31
downloads
0
comments
1999-Marchand-McDevitt-Learning Differential Equations by Exploring Earthquake Induced Structural Vibrations
The project takes full advantage of analytical, numerical, and qualitative techniques to explore the mechanical vibrations of buildings during an earthquake.
earthquake
nondimensionalization
Coulomb damping
mechanical vibration
Modeling Scenario
357
views
245
downloads
1
comments
3-104-BungeeJumping-ModelingScenario
In this project, students design a bungee jumping cord (cross-sectional area and length) that will keep jumpers safe. Students communicate their recommendations as a letter to a client interested in starting a bungee jumping business.
design
falling
mass
spring\
bungee
elesticity
recommendation
consult
Modeling Scenario
245
views
217
downloads
0
comments
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 dynamics
energy
Fluid Mechanics
m
friction
roller coaster
integration by8 parts
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