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2020-Beeken, Paul - First Order Differential Equations - AirResistance
26 Mar 2020 | Contributor(s):: Brian Winkel
Beeken-FirstOrderDifferentialEquations-AirResistanceBeeken, Paul. First Order Differential Equations as applied to Air Resistance. Byram Hills High School.This is a nice and gentle introduction to air resistance modeling.From the Introduction"The problem of air...
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2010-Chicone, C. - Mathematical Modeling and Chemical Kinetics. Notes
26 Mar 2020 | Contributor(s):: Brian Winkel
2010-Chicone-MathModelingANDChemicalKineticsChicone, C. 2010. Mathematical Modeling and Chemical Kinetics. Notes. 14 pp.Motivated by physical science motion laws the author moves into kinetics and life science applications of differential equations.From early section...
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3-015-S-StyrofoamBallFall
24 Mar 2020 | | Contributor(s):: Brian Winkel
We are given data on a falling Styrofoam ball and we seek to model this motion.
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2003-Bohren, Craig F - Dimensional analysis, falling bodies, and the fine art of not solving differential equations
13 Mar 2020 | | Contributor(s):: Brian Winkel
Bohren, Craig F. 2003. Dimensional analysis, falling bodies, and the fine art of not solving differential equations. Am. J. Physics. 72(4): 534-537.See http://pages.erau.edu/~reynodb2/ps303/Bohren_2004_AJP_DimensionalAnalysis.pdf .Abstract: Dimensional analysis is a simple,...
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1-083-S-FallingMeteorites
24 Aug 2019 | | Contributor(s):: Lyle Clifford Smith
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...
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3-009-S-BallDropInWater
16 Dec 2018 | | Contributor(s):: Brian Winkel
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.
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1-063-S-ThreeHoleColumn
15 Dec 2018 | | Contributor(s):: Brian Winkel
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.
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2018-Schneebeli,Hans R. - Modeling Falling Bodies
01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli
Modelling falling bodies is discussed using a computer algebra system-calculator and introducing various traditional and elementary methods from calculus as well as numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...
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2017-Groetsch, C. W. - Hammer and Feather: Some Calculus of Mass and Fall Time
09 Sep 2017 | | Contributor(s):: Brian Winkel
Groetsch, C. W. 2017. Hammer and Feather: Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 3-7.See https://www.tandfonline.com/doi/abs/10.4169/math.mag.90.1.3 .The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA...
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2017-Vas, Lia - Modeling With Differential Equations - notes
05 Sep 2017 | | Contributor(s):: Brian Winkel
Vas, Lia. Notes: Modeling With Differential Equations. 8 pp. http://liavas.net/courses/math422/files/Differential_eq.pdf . Accessed 5 September 2017.This is a set of class notes for Lia Vas in which examples from population, falling objects, tank mixing, growth and threshold, are...
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2017-Benaka, Jan and Sona Ceretkova - Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel.
05 Sep 2017 | | Contributor(s):: Brian Winkel
Benaka, Jan and Sona Ceretkova. 2017. Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel. Spreadsheets in Education. 9(1): Article 3.Abstract: The paper gives the result of an...
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1-115-S-ModelingWithFirstOrderODEs
04 Sep 2017 | | Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model
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3-017-S-StackedCoffeeFiltersFalling
11 Mar 2017 | | Contributor(s):: Brian Winkel
Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered for analysis. Students first form a model using resistance terms. Parameters need to be estimated and models compared.
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2014-Groetsch, C. W. and S. A. Yost. - Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne
02 Mar 2017 | | Contributor(s):: Brian Winkel
Groetsch, C. W. and S. A. Yost. 2014. Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne. The American Mathematical Monthly. 21(6): 499-505.Article Abstract: This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne...
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1999-Brauer, F. - What Goes Up Must Come Down
02 Mar 2017 | | Contributor(s):: Brian Winkel
Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437-440. Article Abstract: NONE This paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum...
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3-070-S-FallingInWater
04 Mar 2016 | | Contributor(s):: Brian Winkel
This is a study of modeling a falling object in liquid. We provide a video (in two versions - .mov and .mp4) which will enable you to collect data on a falling object in water to compare with your model and to estimate parameters using data you can collect from the video. VIDEO Version 1 -...
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3-044-S-DeepWell
30 Aug 2015 | | Contributor(s):: Brian Winkel
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.
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1994-Gruszka, T. - A Balloon Experiment in the Classroom
20 Jun 2015 | | Contributor(s):: T. Gruszka
Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442-444.See https://www.tandfonline.com/doi/abs/10.1080/07468342.1994.11973649 .We quote from the article,“The following experiment involves a balloon, a stopwatch, and a...
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3-019-S-ShuttlecockFall
30 May 2015 | | Contributor(s):: Brian Winkel
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. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and...
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3-013-S-WhiffleBallFall
30 May 2015 | | Contributor(s):: Brian Winkel
We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and apply it to our models.