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##### Includes clear efforts on Issues
Modeling Scenario
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##### 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
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##### 3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped sum of square errors mass spring Hooke's Law oscilation least-squares approximation
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##### 3-101-SpringMassFirstTry-NoResistance-ModelingScenario
Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.
frequency mass oscillation undamped spring constant spring\ Single Degree of Freedom System
Modeling Scenario
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##### 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
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##### 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
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##### 4-039-FallingDarts-ModelingScenario
we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined...
optimization resistance terminal velocity muzzle velocity drag coefficient free fall air drag
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We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process.
DNA\kinetis plasma rat pharmacokinetis
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##### 5-011-ModelingIbuprofren-ModelingScenario
We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the...
data AIC Akaike Information Criterion absorption sum of square errors compartment model ibuprofen delay
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##### 5-022-ColdPill-ModelingScenario
A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation model, use known parameter values, and plot solutions.
rates medicine drug discovery compartment cold pill gastrointestinal bloodstream
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##### 5-030-AirshedSulphur-ModelingScenario
Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of...
sulphur pollution airshed hydrogen sulfide sulfur dioxide
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##### 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
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Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the parameters and estimate these parameters
driver steady state sum of square errors
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##### 4-060-CircuitTuner-ModelingScenario
We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to tune a radio to a certain input frequency.
resistance ciircuit tuned mass tuner frequency Kirchhoff voltage gain frequency response amplitude s Voltage Law inductance capacitor I am currently working in redesining an existing microbiology course. I would like to be part of ed
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##### 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
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