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.
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...
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...
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.
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...
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.
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.
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...
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?''
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.
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.
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...
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....
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...
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...
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...
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...
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.
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...
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...