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Downloads
Views
Date
Relevance
Potential Scenario
153
views
75
downloads
0
comments
2017-David_Morin-Oscillations
So needless to say, an understanding of oscillations is required for an understanding of waves.
damping
frequency response
resonance
oscillation
beats
underdamping
harmonic oscillators
over damping
critical damping
Modeling Scenario
333
views
158
downloads
0
comments
3-102-SpringMassDamped-ModelingScenario
Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.
frequency
mass
oscillation
stiffness
spring constant
spring\
damped
Single Degree of Freedom System
coefficient
Potential Scenario
156
views
48
downloads
0
comments
2009-Reid-King-Pendulum Motion and Differential Equations
This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior.
pendulum
physical pendulum
Modeling Scenario
537
views
1386
downloads
0
comments
5-040-TunedMassDamper-Part-I-Modeling Scenario
We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.
structure
spring-mass-dashpot
spring mass
earthquake
vibration
tuned mass tuner
restoring force
control
dampe
Potential Scenario
126
views
40
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
Modeling Scenario
537
views
294
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
Modeling Scenario
266
views
408
downloads
0
comments
3-087-ThanosPopulationDynamicsInteractingSpecies-ModelingScenario
Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species?
species interactions
predator-prey
competition
Lotka-Volterra
sensitivity analysis
dynamics
population
Potential Scenario
338
views
58
downloads
0
comments
2017-Jun_Liu-Hammer Throwing parameters optimization model research based on flight dynamical differential equation
With progress of times, sports techniques are also rapidly developing, in order to let Chinese hammer throwers more quickly improve themselves levels.
sports
projectile
hammer throw
release angle
Potential Scenario
133
views
73
downloads
0
comments
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.
Accelerometers
free fall
jump
trampoline
Modeling Scenario
209
views
361
downloads
0
comments
4-055-ShatterWineGlass-ModelingScenario
This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?
frequency
damping
amplitude
resonance
oscillation
shattering
wine glass
bridges
aircraft
external force
Potential Scenario
144
views
81
downloads
0
comments
2002-Dietz-Heesterbeek-Daniel Bernoulli-epidemiological model revisited
The seminal paper by Daniel Bernoulli published in 1766 is put into a new perspective. After a short account of smallpox inoculation and of Bernoulli’s life, the motivation for that paper and its impact are described.
life table
epidemic
smallpox
Daniel Bernoulli
competing risk
inoculation
Potential Scenario
109
views
40
downloads
0
comments
2011-Therese-Keane-Combat modelling with partial differential equations
We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.
Lanchester model
troop dynamics
swarming behavior
troop regrouping
losses
non-local terms
local terms
Potential Scenario
110
views
54
downloads
0
comments
2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier analysis or using expensive apparatus.
frequency
resonance
coupled oscillator
Potential Scenario
128
views
34
downloads
0
comments
1999-Long-Weiss-The Velocity Dependence of Aerodynamic Drag A Primer for Mathematicians
This paper is exactly what it says it is, namely, a Primer for Mathematicians. There are ample models, data, attention to such issues as Reynolds’ numbers, and attention to aerodynamics issues.
drag force
aerodynamics
Potential Scenario
254
views
60
downloads
0
comments
1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which chemical processes occur.
kinetics
first order
reaction
second order
zeroth order
Potential Scenario
194
views
60
downloads
0
comments
2013-Gonzalez_Parra-Arenas-Mathematical Model for Social Security Systems with Dynamical Systems
In this paper it is proposed a mathematical approach based on dynamic systems to study the effect of the increase in the Social Security normal retirement age on the worker and on the dynamics of retiree populations.
dynamical systems
retirement model
Social Security
Potential Scenario
132
views
38
downloads
0
comments
1992-CHF_Bulte-The differential equation of the deflection curve
This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint BVP.
beam
deflection
shear force
bending moment
critical load
natural frequency
Potential Scenario
130
views
66
downloads
0
comments
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.
projectile
friction
falling time
rising time
maximum height
Potential Scenario
215
views
46
downloads
0
comments
1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall
We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.
falling
terminal velocity
shuttlecock
vertical fall
Modeling Scenario
307
views
469
downloads
0
comments
6-070-BeerBubbles-ModelingScenario
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
molecular forensics
BEER
sphere
bubble
Newton' Second Law
Ideal Gas Law
drag force
Hadamard
Stokes
mole
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