Tags: medium

Resources (1-20 of 36)

  1. 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.

  2. 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...

  3. 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...

  4. 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.

  5. 10-001-S-TilingHallway

    12 Sep 2019 | | Contributor(s):: Rob Krueger, Eric Stachura

    Students will investigate difference equations through the context of tiling hallways. Students will observe patterns in the tiling which will lead to a difference equation model. Solutions will be calculated by iteration.  Then students will be introduced to the concept of the shift...

  6. 7-040-S-TankInterruptMixing

    22 Aug 2018 | | Contributor(s):: Norman Loney

    We present a 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.

  7. 7-020-S-ThermometerInVaryingTempStream

    22 Aug 2018 | | Contributor(s):: Norman Loney

    We present a 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.

  8. 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...

  9. 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?''

  10. 1-052-S-SaltWaterTanks

    27 Nov 2016 | | Contributor(s):: Brian Winkel

    We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

  11. 6-040-S-StruggleForExistence

    23 Nov 2016 | | Contributor(s):: Brian Winkel

    We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters.

  12. 9-120-S-HorizontalBeam

    22 Nov 2016 | | Contributor(s):: Gregg Waterman, Tiernan R Fogarty

    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions. Vertical deflection occurs as a result of the weight of the beam alone, with no compressive force at the ends or distributed...

  13. 7-010-S-MultipleDoses

    12 Oct 2016 | | Contributor(s):: Brian Winkel

    Two possible multiple dose drug administration regimens are offered for modeling. 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 the other involves steady drip flow over short periods of time....

  14. 1-039-S-StochasticPopModels

    11 Sep 2016 | | Contributor(s):: Dan Flath

    We offer students the opportunity to develop several strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t. We go further...

  15. 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...

  16. 1-036-S-NeutralBuoyancy

    03 Jun 2016 | | Contributor(s):: John Thomas Sieben

    Things float or they don’t.  Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...

  17. 1-041-S-AirToTop

    19 May 2016 | | Contributor(s):: John Thomas Sieben

    Divers, especially novice divers, have concerns about running out of breathing air while at depth.  One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using...

  18. 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.

  19. 1-029-S-ConeToCubeFlow

    02 Mar 2016 | | Contributor(s):: Sania Qureshi

    We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom  is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

  20. 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...