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Modeling Scenario
358
views
351
downloads
0
comments
4-039-FallingDarts-ModelingScenario
we develop, solve, and analyze a second order differential equation model for free fall incorporating air resistance. Students solve the model using two methods -- reduction of order and separation of variables, and method of undetermined...
optimization
resistance
terminal velocity
muzzle velocity
drag coefficient
free fall
air drag
Modeling Scenario
357
views
284
downloads
0
comments
3-011-EulerBallThrowing-ModelingScenario
If a tennis ball is thrown through the air it will hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the...
coding
dragon
Vectors
Euler's method
ball
Modeling Scenario
249
views
190
downloads
0
comments
1-083-FallingMeteorites-ModelingScenario
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...
falling object
drag
variable mass
factor ranking
meteor
meteorite
Modeling Scenario
287
views
193
downloads
0
comments
3-055-FloatingBox-ModelingScenario
In this scenario, we lead students through the process of building a mathematical model for a floating rectangular box that is bobbing up and down.
oscillation
Archimedes’ Principle
buoancy
oscillatory motion
Newton's Second Law
Modeling Scenario
246
views
208
downloads
0
comments
3-110-MilitarySpringMassApplication-ModelingScenario
The is a collection of different scenarios for the shock system of a trailer. In each scenario, students will transform the shock system of a trailer into a second-order differential equation, solve, and interpret the results.
damping
resonance
beats
spring-mass system
Laplace Transfom
Dirac Delta function
Modeling Scenario
280
views
167
downloads
0
comments
3-045-RampBounce-ModelingScenario
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.
projectile motion
inclined ramp
coefficient of restitution
optimal angle
bounce
Modeling Scenario
335
views
136
downloads
0
comments
1-115-ModelingWithFirstOrderODEs-ModelingScenario
Several models using first order differential equations are offered with some questions on formulating a differential equations model with solutions provided.
bacteria
falling object
Newton's Law of Cooling
drug
cooling
drag
Modeling Scenario
243
views
123
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
296
views
400
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
333
views
156
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
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