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Downloads
Views
Date
Relevance
Potential Scenario
130
views
66
downloads
0
comments
1999-F_Brauer-What Goes Up Must Come Down
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 height than it takes to rise to this maximum height for frictional forces.
projectile
friction
falling time
rising time
maximum height
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
513
views
178
downloads
0
comments
3-033-S-TimeUpTimeDown-ModelingScenario
We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
projectile motion
apex
vertical motion
Potential Scenario
275
views
56
downloads
0
comments
2012-Hassan_Moore-Using projects to stimulate learning in mathematics and engineering mathematics courses
Given that time is a premium in the academy and project creation is a time consumer, three original projects, which may be injected into any Calculus III, Differential Equations, or Engineering Mathematics course, have been created.
solutions
class projects
physical phenomenon
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
290
views
208
downloads
0
comments
3-044-DeepWell-ModelingScenario
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.
gravity
projectile motion
falling body
speed of sound
Potential Scenario
168
views
59
downloads
0
comments
2017-CW_Groetsch-Hammer and Feather - Some Calculus of Mass and Fall Time
Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a falcon feather on the surface of the moon to give a dramatic illustration that this is not so.
gravity
free fall
linear resistance
quadratic resistance
hammer
feather
Moon resistance
Galileo
Potential Scenario
151
views
95
downloads
0
comments
2014-John_Cimbala-Dynamic System Response
In this learning module, we discuss the dynamic system response of sensors and their associated electronic circuits.
sensor networks
oscillations
system response
electronic circuit
Potential Scenario
201
views
54
downloads
0
comments
2009-Shamim-EtAl-Investigating viscous damping using a webcam
We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped, critically damped and underdamped regimes of harmonic motion.
laboratory
underdamped
overdamped
critically damped
harmonic motion
image processing
viscous fluid
Article or Presentation
165
views
56
downloads
0
comments
1994-T_Gruszka-A_Balloon_Experiment_in_the_Classroom
The experiment consists of dropping a balloon from two different heights and recording the time it takes to hit the floor. The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick.
differential equations
resistance
gravity
free fall
acceleration
balloon
Modeling Scenario
305
views
264
downloads
0
comments
3-013-WhiffleBallFall-ModelingScenario
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.
Akaike Information Criterion
resistance
gravity
Free Body Diagram
force
falling object
Whiffle ball
Article or Presentation
140
views
50
downloads
0
comments
2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
resistance
projectile motion
projectile
fluid
Mersenne
Modeling Scenario
389
views
418
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
Potential Scenario
258
views
88
downloads
0
comments
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.
Hangtime
Tauberian Identities
Road Runner
Wile E. Coyote
Potential Scenario
142
views
50
downloads
0
comments
2014-Groetsch-Yost-Vertical Projection in a Resisting Medium - Revelations on Observations of Mersenne
This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
resistance
projectile
Potential Scenario
336
views
95
downloads
0
comments
2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.
kinetics
chemical kinetics
zeroth order reaction
first order reaction
second order reaction
Modeling Scenario
993
views
1536
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
387
views
549
downloads
0
comments
3-019-ShuttleCockFalling-ModelingScenario
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.
resistance
gravity
Free Body Diagram
shuttlecock
fallingc object
Modeling Scenario
245
views
141
downloads
0
comments
3-027-BobbingDropping-ModelingScenario
We present two exercises in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
drug resistance
directed
buoyancy
free fall
static equilibrium
displacement
Modeling Scenario
356
views
215
downloads
0
comments
3-054-Relay-ModelingScenario
We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.
distance
projectile motion
relay
time
baseball
outfield
home plate
minimization
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