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## Resources

##### Includes clear efforts on Issues
Modeling Scenario
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##### 3-017-StackedCoffeeFiltersFalling-ModelingScenario
Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.
data falling body coffee filter stacked ersistance
Modeling Scenario
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##### 3-019-ShuttleCockFalling-ModelingScenario
We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models.
resistance gravity Free Body Diagram shuttlecock fallingc object
Modeling Scenario
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##### 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
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##### 3-029-FerrisWheelCatch-ModelingScenario
We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.
parametric equations projectile motion initial velocity ferris wheel catch collision
Modeling Scenario
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For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?
projectile motion baseball parametric equation stadium home run no reistant fairness no resistance
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##### 3-040-FirstPassageTime-ModelingScenario
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
oscillator damped underdamped first passage first passage time spring mash dashpot
Modeling Scenario
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##### 3-041-UpDown-ModelingScenario
Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.
gravity projectile motion falling body maximum heightf timing
Modeling Scenario
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##### 3-054-Relay-ModelingScenario
We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.
distance projectile motion relay time baseball outfield home plate minimization
Modeling Scenario
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##### 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 Archimedesâ€™ Principle buoancy oscillatory motion Newton's Second Law
Modeling Scenario
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##### 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
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##### 3-067-RLCSeriesCircuit-ModelingScenario
In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical...
resistance Multisim circuit RLC circuit inductance capacitance cimulation governing equation
Modeling Scenario
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##### 3-071-WirelessTelegraphy-ModelingScenario
This project has three parts, (1) done at home, (2) and (3) in class. In (1) we recall how to solve second order differential equations with constant coefficients and simple source functions. In class understand resonance and beats.
b RLC circuit resonance beats current wireless telegraphy LC circuit
Modeling Scenario
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##### 3-072-EarthQuakePartI-ModelingScenario
This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.
earthquake vibration amplitude resonance undamped spring-mass system
Modeling Scenario
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##### 3-073-EarthQuakePartII-ModelingScenario
Your goal here is to determine how much friction/damping should be designed into a building to keep the roof from moving too far (which would result in the entire building collapsing) when it undergoes minor vibrations from a small earthquake.
earthquake vibration damping amplitude spring-mass system steady-state solution underdamped
Modeling Scenario
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