## Resources

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Resource Type (84)

Modeling Scenario(47) Potential Scenario(29) Article or Presentation(3) Free Online Textbook(5)

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Differential Equation Type (84)

ODE(81) PDE(2) Difference(1) Delay(2) Integral(1) First(19) Second(54) Higher(1) Linear(41) Nonlinear(16) System(24) Constant Coeff(24) Homogeneous(19) Nonhomogeneous(18) Other(1)

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Technique (84)

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Qualitative Analysis (84)

Equilibrium(5) Stability(5) Phase Plane(3) Graphical analysis(29) Eigenvalue analysis(2) Parameters(55) Other(17)

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Application Area (84)

Chemistry(10) Economics(2) Engineering(28) Life Sciences(15) Mathematics(36) Modeling (general)(72) Physics(50) Social Sciences(3)

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Precalculus(1) Calculus 2(21) Calculus 3 (multivariable)(1) Differential Equations(82) Modeling(82)

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Introductory(81) Upper Level(77) High School(48)

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Reviewing prior research(4) Asking a question(45) Formulating hypotheses(41) Designing/conducting experiments(5) Predicting outcomes(16) Gathering data/making observations(12) Analyzing data(20) Interpreting results/data(20) Displaying/modeling results/data(20) Communicating results(21) Translating into mathematics(5)

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Assessment Type (47)

Assessment of individual student performance(1) Assessment of student groups/teams(1) Homework(40) Give an oral presentation(1) Informal in-class report(1) Written assignment: Report(45)

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Pedagogical Approaches (44)

Case Study(2) Collaborative Work(1) Computer Model(3) Physical Model(2) Guided inquiry/investigation(40)

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Vision and Change Core Competencies - Ability (47)

Create and develop models(45) Use quantitative reasoning(42) Design simulations(9) Tap into interdisciplinary study(10) Communicate and collaborate with mathematics community(2) Communicate and collaborate with other disciplines(5)

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Principles of How People Learn (47)

Motivates student to learn material(46) Focuses student on the material to be learned(46) Develops supportive community of learners(2) Leverages differences among learners(1) Reveals prior knowledge(2) Requires student to do the bulk of the work(2)

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Bloom's Cognitive Level (43)

Application & Analysis(42) Synthesis/Evaluation/Creation(1)

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Includes clear efforts on Issues (0)

###### Applied Filters

Modeling Scenario

##### 3-010-EnergyInSpringMassSystem-ModlingScenario

As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.Modeling Scenario

##### 5-014-TwoSpringMass-ModelingScenario

We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.Modeling Scenario

##### 1-019-RocksInTheHead-Modeling Scenario

We describe an experiment with data on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. Students use the logistic differential equation as a reasonable model and estimate parameters.Modeling Scenario

##### 3-001-SpringMassDataAnalysis-ModelingScenario

We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass configuration and estimation of parameters are the core.Modeling Scenario

##### 3-102-SpringMassDamped-ModelingScenario

Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.Potential Scenario

##### 2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics

The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.Potential Scenario

##### 2009-Chellaboina-EtAl-Modeling And Analysis-Mass Action Kinetics

Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of reactions, that is, reaction networks. These models are a special form of compartmental systems, involving mass- and energy-balance relations.Potential Scenario

##### 1989-R_Blickhan-Spring Mass Model For Running-Hopping

A simple springâ€”mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.Modeling Scenario

##### 5-040-TunedMassDampers-PartII-ModelingScenario

Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a spring-mass-dashpot with stiffness replacing spring...Modeling Scenario

##### 3-002-ModelsMotivatingSecondOrder-ModelingScenario

Ordinary differential equations involve second derivatives and second derivatives appear in many contexts, chief among them are the study of forces and resulting motion. This is principally because of Newton's Second Law of Motion.Article or Presentation

##### 2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts

We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.Modeling Scenario

##### 3-091-SpringModeling-ModelingScenario

In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical onesâ€”giving them an opportunity to actually test a model against data.Modeling Scenario

##### 3-101-SpringMassFirstTry-NoResistance-ModelingScenario

Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.Potential Scenario

##### 2017-Guy-Bart_Stan-Modelling in Biology

This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.Potential Scenario