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Downloads
Views
Date
Relevance
Technique Narrative
474
views
111
downloads
0
comments
7-005-OverViewLaplaceTransforms-TechniqueNarrative
This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.
integration
Laplace transform
Inverse Laplace transofrm
integration by parts
Modeling Scenario
363
views
331
downloads
0
comments
7-040-TankInterruptMixing-ModelingScenario
We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.
Laplace transform
inverse Laplace Transform
salt
tank
mixing
interrupt
Technique Narrative
757
views
222
downloads
0
comments
7-006-LaplaceTransformBirth-TechniqueNarrative
We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
Transformations
power series
Modeling Scenario
308
views
125
downloads
0
comments
5-036-HalfCarVibration-ModelingScenario
Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...
vibration
vehicle
half-car model
finite element analysis
shock absorbers
suspension
Modeling Scenario
308
views
239
downloads
0
comments
7-010-MultipleDoses-ModelingScenario
Two multiple dose drug administration regimens are offered. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and another involves steady drip flow...
drug discovery
step function
dose
Dirac
drug administration
inverse Laplace Transform
intraveneous
bolus
steady drip
Modeling Scenario
253
views
246
downloads
0
comments
7-020-ThermometerInVaryingTempStream-ModelingScenario
We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
temperature
steady state
thermometer
heat exchange
transfer function
phase lag
Invers Laplace Transform
Modeling Scenario
442
views
263
downloads
0
comments
7-011-CoupledSystemLaplace-ModelingScenario
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
transfer function
polycarbonate
baby heater
coupled system
heating
Modeling Scenario
236
views
332
downloads
0
comments
9-125-BeamModeling-ModelingScenario
This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
Fluid Mechanics
beam
cantilever
impulse
Laplace transform
boundary condition
fourth order
Modeling Scenario
398
views
176
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
Modeling Scenario
225
views
335
downloads
0
comments
9-015-UnearthingTruth-ModelingScenario
This project introduces \textit{electrical resistivity tomography}, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current.
geophysical
Imaging
Statistical inverse problem
tunnel
conduction
Holocaust
Vilnius
Divergence Theorem
flux
Laplace's equation
impedance
electrical resistivity tomography
tomography
resistivity
Modeling Scenario
430
views
261
downloads
0
comments
3-092-WirelessPower-ModelingScenario
We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
DESMOS
wireless power transmission
electric circuits
Kirchhoff's Voltage Law
Modeling Scenario
246
views
208
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
835
views
696
downloads
0
comments
4-023-MysteryCircuit-ModelingScenario
Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.
filters
circuit
RLC circuit
Kirchhoff
voltage
gain
driver
Modeling Scenario
306
views
232
downloads
0
comments
1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Variance
Mean
stochastic
random
operations research
industrial engineering
Poisson process
traffic
Modeling Scenario
276
views
169
downloads
0
comments
3-026-SpringInverseProblem-ModelingScenario
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
data
mass
inverse problem
spring\
parameter estimate
Modeling Scenario
288
views
195
downloads
0
comments
3-130-MatterOfSomeGravity-ModelingScenario
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
gravity
inverse problem
acceleration
Modeling Scenario
187
views
164
downloads
0
comments
3-150-ItsABlastFurnace-ModelingScenario
This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.
steady state
heat equation
inverse problem
furnace
Modeling Scenario
269
views
210
downloads
0
comments
6-018-ExploringSIRModel-ModelingScenario
Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models.
population dynamics
sensitivity
disease
SIR models
epidemic
rumors
Modeling Scenario
210
views
239
downloads
0
comments
4-036-AltitudeDependentGravity-ModelingScenario
When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
a
gravity
projectile
linearization
ltitufe
altitude
Modeling Scenario
989
views
2108
downloads
0
comments
3-030-SecondOrderIntro-ModelingScenario
We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.
parameter estimation
non-homogeneous
Spanish
frequency
buoyancy
inverse problem
thrust
underdamped
first passage
spring mash dashpot
real
complex
homogeneous
superposition
parachute
overdamped
critically damped
buoy
quadratic equation
roots
rocket flight
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