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Downloads
Views
Date
Relevance
Modeling Scenario
258
views
220
downloads
0
comments
1-120-CircularRollerCoaster-ModelingScenario
Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
population dynamics
energy
Fluid Mechanics
m
friction
roller coaster
integration by8 parts
Modeling Scenario
216
views
121
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
212
views
157
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
220
views
235
downloads
0
comments
3-035-StadiumDesign-ModelingScenario
For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?
projectile motion
baseball
parametric equation
stadium
home run
no reistant
fairness
no resistance
Modeling Scenario
174
views
96
downloads
0
comments
3-041-UpDown-ModelingScenario
Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.
gravity
projectile motion
falling body
maximum heightf
timing
Modeling Scenario
166
views
274
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
171
views
134
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
162
views
302
downloads
0
comments
5-090-SolidParticleErosion-ModelingScenario
By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.
classical mechanics
solid mechanics
Newton's Laws of Motion
rigid body
plasticity
pitting
ductile surface
Modeling Scenario
295
views
533
downloads
0
comments
1-155-CruiseControl-ModelingScenario
In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
PID controller
feedback control
Control theory
cruise control
automobile
closed-loop control
input-ouput
block diagram
Potential Scenario
123
views
57
downloads
0
comments
2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
kinematics
curve design
highway exit
tangential acceleration
Potential Scenario
119
views
42
downloads
0
comments
2012-Rusinko-Swan-Agent-Based Fabric Modeling Using Differential Equations
We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system.
NetLogo
spring mass
agent-based
draping
yarn
fabric
Potential Scenario
122
views
47
downloads
0
comments
2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus
We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.
calculus
Flight
projectile
water rocket
Potential Scenario
90
views
33
downloads
0
comments
2005-P_Howard-Modeling with ODE
In these notes we consider three critical aspects in the theory of ordinary differential equations: developing models of physical phenomena, mathematically well-posed, solving ODE numerically .
Fluid Mechanics
compartment
populations
variational methods
Hamiltonian mechanics
Technique Narrative
271
views
143
downloads
0
comments
1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Modeling Scenario
917
views
1428
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
233
views
231
downloads
0
comments
3-029-FerrisWheelCatch-ModelingScenario
We offer the opportunity to model the throw of an object to a person on a moving Ferris wheel.
parametric equations
projectile motion
initial velocity
ferris wheel
catch
collision
Modeling Scenario
168
views
81
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Modeling Scenario
168
views
131
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
243
views
246
downloads
0
comments
6-002-EulerCromerPendulum-ModelingScenario
This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
pendulum
semi-implicit methods
Euler-Cromer
numerical solvers
Modeling Scenario
154
views
315
downloads
0
comments
4-055-ShatterWineGlass-ModelingScenario
This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?
frequency
damping
amplitude
resonance
oscillation
shattering
wine glass
bridges
aircraft
external force
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