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Downloads
Views
Date
Relevance
Modeling Scenario
315
views
182
downloads
0
comments
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.
energy
mass-spring system
kinetic energy
potential energy
total energy
Modeling Scenario
249
views
193
downloads
0
comments
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.
mass
spring mass damper
springs
Modeling Scenario
296
views
302
downloads
0
comments
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.
logistic growth
parameter estimation
experiment
Modeling Scenario
386
views
414
downloads
0
comments
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.
data
damping
spring-mass system
Newton's Second Law of Motion
spring constant
Hooke's Law
Modeling Scenario
326
views
154
downloads
0
comments
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.
frequency
mass
oscillation
stiffness
spring constant
spring\
damped
Single Degree of Freedom System
coefficient
Modeling Scenario
329
views
387
downloads
0
comments
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...
structure
resistance
spring-mass-dashpot
earthquake
vibration
control
damping
tuned mass damper
stiffness
reduction of vibration
Modeling Scenario
606
views
815
downloads
0
comments
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.
resistance
spring mass
oscillation
Hooke's Law
dampening
Modeling Scenario
264
views
140
downloads
0
comments
3-091-SpringModeling-ModelingScenario
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.
data
laboratory
LoggerPro
Vernier
mass-spring system
model validation
empirical model
theoretical model
Modeling Scenario
392
views
413
downloads
0
comments
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.
frequency
mass
oscillation
undamped
spring constant
spring\
Single Degree of Freedom System
Modeling Scenario
293
views
386
downloads
0
comments
3-060-DataToDifferentialEquation-ModelingScenario
Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.
Association & Data Fitting
mass
spring-mass system
spring\
total distance
numerical differentiation
Modeling Scenario
209
views
138
downloads
0
comments
3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.
mass
undamped
Free Body Diagram
springs
two springs
oscil
lation
spring constant
fixed ends
Modeling Scenario
529
views
1337
downloads
0
comments
5-040-TunedMassDamper-Part-I-Modeling Scenario
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.
structure
spring-mass-dashpot
spring mass
earthquake
vibration
tuned mass tuner
restoring force
control
dampe
Modeling Scenario
840
views
490
downloads
0
comments
1-012-Sublimation-Modeling Scenario
We offer data on the sublimation of dry ice (carbon dioxide) collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the...
sublimation
dry ice
Modeling Scenario
286
views
163
downloads
0
comments
3-009-BallDropInWater-ModelingScenario
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.
resistance
gravity
falling body
terminal velocity
buoyancy
Modeling Scenario
271
views
159
downloads
0
comments
3-026-SpringInverseProblem-ModelingScenario
We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
data
mass
inverse problem
spring\
parameter estimate
Modeling Scenario
252
views
325
downloads
0
comments
3-072-EarthQuakePartI-ModelingScenario
This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.
earthquake
vibration
amplitude
resonance
undamped
spring-mass system
Modeling Scenario
988
views
1535
downloads
0
comments
3-016-FallingCoffeeFilters-ModelingScenario
We are given data on the time and position of a stack of coffee filters as it falls to the ground. We attempt to model the falling mass and we confront the different resistance terms and models.
resistance
Free Body Diagram
coffee filter
force
graviity
falling object
Modeling Scenario
340
views
269
downloads
0
comments
3-017-StackedCoffeeFiltersFalling-ModelingScenario
Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.
data
resistance
falling body
coffee filter
stacked
Modeling Scenario
239
views
117
downloads
0
comments
3-040-FirstPassageTime-ModelingScenario
We apply the notions of dampedness to second order, linear, constant coefficient, homogeneous differential equations used to model a spring mass dashpot system and introduce the notion of first passage time through 0 value with several applications.
oscillator
damped
underdamped
first passage
first passage time
spring mash dashpot
Modeling Scenario
256
views
208
downloads
0
comments
3-105-FrequencyResponse-ModelingScenario
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.
transient dynamics
circuit
spring mass
driver
frequency response
amplitude
steady state
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