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2020-Shelton, Therese - Remote Teaching Module - Car Suspensions
28 Jul 2020 | | Contributor(s):: Therese Shelton
In this modeling activity, students examine the spring-mass-dashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is installed....
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3-105-S-FrequencyResponse
22 Jul 2020 | | Contributor(s):: Brian Winkel
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.
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3-034-S-CarSuspensions
14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel
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.
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3-027-S-BobbingDropping
10 Jul 2020 | | Contributor(s):: Brian Winkel
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
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1-088-S-RoomTemperature
15 Jun 2020 | | Contributor(s):: Tracy Weyand
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...
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1-136-S-MarriageAge
11 Jun 2020 | | Contributor(s):: Tracy Weyand
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. This model comes from a paper by Hernes and, in this project, is compared to another model used by Coale.These models are first-order ordinary differential equations (which...
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1-128-S-RocketFlight
04 Jun 2020 | | Contributor(s):: Brian Winkel
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.
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3-031-S-SpringCost
28 May 2020 | | Contributor(s):: Brian Winkel
This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.
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6-070-S-BeerBubbles
24 Apr 2018 | | Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...
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1-042-S-Kool-Aid
26 Apr 2017 | | Contributor(s):: Kristin Burney, Lydia Kennedy, Audrey Malagon
Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing...
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1-014-S-DrainingContainers
17 Mar 2017 | | Contributor(s):: Brian Winkel
We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''
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1-033-S-SouthernBarbeque
22 Jun 2016 | | Contributor(s):: Troy Henderson
We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat. This data can be used to model and predict the amount...
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1-032-S-WordPropagation
07 Apr 2016 | | Contributor(s):: Rachelle DeCoste, Rachel Bayless
This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.
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1-055-S-WaterFallingInCone
27 Feb 2016 | | Contributor(s):: Brian Winkel
There are three videos associated with this Modeling Scenario and all are available on SIMIODE YouTube Channel: Capture-3 YouTube Version SlowMoCapture-1 YouTube Version SlowMoCapture-2 YouTubeVersion and as streaming videos or down loads in this Modeling Scenario under the Supporting Docs Tab...
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1-034-S-FishMixing
24 Dec 2015 | | Contributor(s):: Eric Sullivan, Elizabeth Anne Carlson
This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...
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1-011A-S-Kinetics
06 Jun 2015 | | Contributor(s):: Karen Bliss
Adapted from 1-11-Kinetics, SIMIODE modeling scenario. We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...
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1-027-S-StochasticProcesses
04 Jun 2015 | | Contributor(s):: Brian Winkel
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. We work to build our model of random events which...
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1-023-S-RumorSpread
04 Jun 2015 | | Contributor(s):: Brian Winkel
We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.
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1-020-S-IceMelt
04 Jun 2015 | | Contributor(s):: Brian Winkel
We offer up the claim of a store catalog that its ice ball mold allows users to "... make ice balls that outlast cubes and won't water drinks down." We ask students to build a mathematical model to defend or contradict this claim.
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1-019-S-RocksInTheHead
04 Jun 2015 | | Contributor(s):: Brian Winkel
We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...