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Downloads
Views
Date
Relevance
Potential Scenario
111
views
34
downloads
0
comments
2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
Walk through the cases in context of second order linear constant coefficient differential equation with driving function
driving function
viscous
mechanical system
Modeling Scenario
196
views
209
downloads
0
comments
4-050-ResonanceBeats-ModelingScenario
We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
Spring 2020 workshop
vibration
tuning
driver
resonance
forced vibration
undamped
beats
naturl frequency
Modeling Scenario
242
views
196
downloads
0
comments
3-105-FrequencyResponse-ModelingScenario
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
transient dynamics
circuit
spring mass
driver
frequency response
amplitude
steady state
Modeling Scenario
226
views
181
downloads
0
comments
3-110-MilitarySpringMassApplication-ModelingScenario
The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation, solve, and interpret the results.
damping
resonance
beats
spring-mass system
Laplace Transfom
Dirac Delta function
Modeling Scenario
500
views
1247
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
Modeling Scenario
187
views
280
downloads
0
comments
3-064-GearTrain-ModelingScenario
Students model an input-output mechanical system of gears with a second order, non-homogeneous, ordinary differential equation with constant coefficients. The model incorporates friction and moments of inertia of the gear train components.
friction
gear
spur gear
gear train
torque
gear ratio
angular acceleration
angular velocity
moment of inertia
double reduction gear
Article or Presentation
175
views
51
downloads
0
comments
2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
optimization
discovery
Fourier
Fourier seris
Potential Scenario
144
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
377
views
254
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
Potential Scenario
239
views
36
downloads
0
comments
2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
predator-prey
harvesting
Pontryagin’s maximum principle
bioeconomic
bionomic equilibrium
biotechnical productivity
catch-rate function
optimal equilibrium
Potential Scenario
164
views
44
downloads
0
comments
2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.
sustainability
fish
Fishing
management
harvest
fisher
strategy
overfishing
Modeling Scenario
703
views
679
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
Potential Scenario
131
views
50
downloads
0
comments
2016-Lewnard-Townsend-Climatic and evolutionary drivers of phase shifts in the plague epidemics of colonial India
Our analysis shows that historical datasets can yield powerful insights into the transmission dynamics of reemerging disease agents with which we have limited contemporary experience to guide quantitative modeling and inference.
infectious disease
p
Vector-Borne Disease
lague
plague
Potential Scenario
146
views
81
downloads
0
comments
2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
kinematics
curve design
highway exit
tangential acceleration
Modeling Scenario
628
views
539
downloads
0
comments
1-032-WordPropagation-ModelingScenario
This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
Google
exponential growth
language
word problems
etymology
Ngram
propagation
Jumbo
Modeling Scenario
379
views
156
downloads
0
comments
7-008-MachineReplacement-ModelingScenario
Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
Probability
replacement number
Laplace transform
industrial engineering
machine
convolution
distributioj
step function
derivative definition
Article or Presentation
164
views
46
downloads
0
comments
2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
circuit
Laplace transform
transfer function
mystery circuit
voltage frequency
two loop circuit
Potential Scenario
156
views
64
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometric Functions
circle
squigonometry
inverse function
trigonmetry
Potential Scenario
127
views
48
downloads
0
comments
2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
Expected Value
Riemann sum
net change
Potential Scenario
140
views
31
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometry
Trigonometric Functions
parametric equations
circle
sine
cosine
squigonometry
inverse function
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