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Downloads
Views
Date
Relevance
Potential Scenario
150
views
71
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
282
views
182
downloads
0
comments
3-055-FloatingBox-ModelingScenario
In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.
oscillation
Archimedes’ Principle
buoancy
oscillatory motion
Newton's Second Law
Potential Scenario
160
views
40
downloads
0
comments
2013-Boscolo-Stellato-Undergraduate study of harmonic and parametric motion of a simple spring-mass system from motion waveforms
In this paper, we describe a laboratory exercise that caters to beginning students while giving those with more background an opportunity to explore more complex aspects of the motion.
laboratory
experiment
spring mass
air friction
apparatus
waveforms
Free Online Textbook
123
views
50
downloads
0
comments
1991-Carmine_Chicone-Ordinary Differential Equations with Applications
This is a complete text for a graduate level course. Hence there is much theory, but there is a chapter on applications with some sophisticated approaches and high level modeling of motion.
orbits
two mass system
atom
magnetic field
coupled pendulum
inverted pendulum
charged particle
Kepler motion
Potential Scenario
168
views
78
downloads
0
comments
2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics
This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.
projectile
air resistance
free fall
drag
harmonic oscillation
Modeling Scenario
1147
views
623
downloads
0
comments
3-065-UpDown-ModelingScenario
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.
terminal velocity
Newton's Second Law of Motion
velocity
motion
apex
Free Online Textbook
158
views
52
downloads
0
comments
2017-Craig_Tracy-Lectures on Differential Equations
These notes are for a one-quarter course in differential equations. The approach is to tie the study of differential equations to specific applications in physics with an emphasis on oscillatory systems.
physics
oscillation
Modeling Scenario
215
views
279
downloads
0
comments
5-015-RunnersSynchronize-ModelingScenario
In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena.
predator
Autonomous equations
oscillation
coupled oscillator
synchrony
runner
prey
Kuramato model
Modeling Scenario
338
views
215
downloads
0
comments
1-043-CoolingUpAndDown-ModelingScenario
We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.
temperature
oscillation
Newton's Law of Cooling
cooling
thermostat
air conditioner
Potential Scenario
193
views
49
downloads
0
comments
2009-Shamim-EtAl-Investigating viscous damping using a webcam
We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped, critically damped and underdamped regimes of harmonic motion.
laboratory
underdamped
overdamped
critically damped
harmonic motion
image processing
viscous fluid
Potential Scenario
132
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
Potential Scenario
137
views
82
downloads
0
comments
2017-Bruce_Emerson-Wonderful World of Differential Equations
This is a terrific set of noted with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
Newton's Second Law of Motion
Newton's Law of Cooling
reactions
Poiseuille’s Law
stopping distance
rate of change
problems
modeling opportunities
Potential Scenario
157
views
65
downloads
0
comments
2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
Newton's Second Law of Motion
Newton's Law of Cooling
biochemical reactions
Poiseuille’s Law
stopping distance
Potential Scenario
108
views
59
downloads
0
comments
2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
This article describes an equation of motion for a waggling pendulum.
resonance
inverted pendulum
mechanics
damped pendulum
Potential Scenario
118
views
61
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.
spring mass
oscillation
Hooke's Law
coupled springs
periodic
forcing function
phase portrait
Potential Scenario
152
views
46
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
Potential Scenario
136
views
79
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
Modeling Scenario
335
views
392
downloads
0
comments
3-006-Buoyancy-ModelingScenario
We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.
data collection
experiment
buoyancy
Newton's Second Law of Motion
Modeling Scenario
291
views
386
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
201
views
210
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
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