5-020-ParacetamolAbsorption-ModelingScenario

09 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/S905-RF31

We offer drug absorption data on paracetamol, an analgesic pain reliever, for two different sets of patients, vegetarian and non-vegetarian. Students build a two compartment model for plasma and non-plasma (tissue) compartments of human patients.

7-010-MultipleDoses-ModelingScenario

09 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/CCW1-E736

Two multiple dose drug administration regimens are offered. 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 another involves steady drip flow over time.

4-035-ParEstSteadyState-ModelingScenario

09 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/ZP3P-JD54

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

4-050-ResonanceBeats-ModelingScenario

09 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/QVX4-5091

We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.

4-060-CircuitTuner-ModelingScenario

08 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/SBYS-E350

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.

6-021-AcornsRodentsSnakes-ModelingScenario

08 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/51E8-TF36

Students are given the opportunity to build a three tropic level model in which snakes eat rodents, rodents eat acorns, and acorns grow and occasionally mast.

3-105-FrequencyResponse-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/CWSK-4W89

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.

3-070-FallingInWater-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/HQKK-1E21

We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters.

3-063-FallingBuildingIce-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/YHWS-5640

We model the fall of a piece of ice which is falling from a high building in New York City.

3-045-RampBounce-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/9CYZ-J044

Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.

3-044-DeepWell-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/1MZA-4X06

We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.

3-020-ChordPathTime-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/AX0T-G678

Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.

4-023-MysteryCircuit-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/HDA6-G326

Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.

1-125-DiceyPopulation-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/VWKS-2C93

We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters.

1-107-ClothDry-ModelingScenario

07 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/25MZ-WH32

We build a mathematical model for the rate of drying in a wet cloth while hanging in air. A model can be based on underlying physical principles (analytic) or based on observations and reasoned equations, but no physical assumptions (empirical).

7-008-MachineReplacement-ModelingScenario

06 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/N3RA-R937

Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.

9-012-PDEGuitarTuning-ModelingScenario

06 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/SCCE-AK14

We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.

5-040-TunedMassDamper-Part-I-Modeling Scenario

06 May 2022 | Contributor(s): Brian Winkel, Keith Landry | doi:10.25334/V09Q-6M70

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.

1-007-AntTunnelBuilding-ModelingScenario

06 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/D9PB-4P37

We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill.

5-026-Evictions-MmodelingScenario

22 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/1998-8110

In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .

6-040-StruggleForExistence-ModelingScenario

05 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/G26Z-AM66

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

1-005-OilSlick-ModelingScenario

05 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/C5NK-7H32

We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.

5-007-ChemOpt-ModelingScenario

05 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/DC53-EK89

Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.

5-005-Dialysis-ModelingScenario

05 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/D0C7-3857

We design a compartment model of a kidney dialysis machine and compare 3 and 9 compartments for the machine as well as determine the effect of change in one of the parameters in the model on the effectiveness to deliver quality dialysis.

6-005-InsectColonySurvivalOpt-ModelingScenario

04 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/FPWS-2554

We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.