Keywords: Non-Linear Systems (19)

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Ball in a Wedge Model
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Ball in a Wedge Model

The Ball in a Wedge model displays a ball confined to move ... (more)

The Ball in a Wedge model displays a ball confined to move between two walls that form a wedge shape. The ball undergoes elastic collisions with the walls of the wedge. The angle of the wedge can be changed by setting the angle with the text box or dragging one of the wedge walls. By clicking in the Poincare section you can set the initial conditions of the motion of the ball. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Ball in a Wedge model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_mech_chaosWedge.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for Newtonian mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Technology
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Wolfgang Christian
Chaos - Chaotic Pendulum Experiment
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Chaos - Chaotic Pendulum Experiment

Website containing LabVIEW programs, student writeup and auxiliary material for an experiment ... (more)

Website containing LabVIEW programs, student writeup and auxiliary material for an experiment on a chaotic pendulum. The writeup includes instructions for the acquisition, display, analysis, and simulation of chaotic data sets. (less)

Subject:
Mathematics
Physics
Technology
Material Type:
Activities and Labs
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Robert DeSerio
Chaos and Non-Linear Physics
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Chaos and Non-Linear Physics

In this experiment, we will discover: 1. how very simple systems can ... (more)

In this experiment, we will discover: 1. how very simple systems can exhibit complex behavior under certain conditions, 2. the richness of the mathematical and physical structure of dynamical systems, 3. how an arbitrarily small change in the input can change the long-term conduct of a dynamical system drastically, 4. how to construct and interpret phase portraits and Poincare Maps for different kinds of responses of a system, 5. the mystery of Fiegenbaum constant and what makes chaos a universal underlying structure of the complexity exhibited by nonlinear dynamical systems, 6. a beautiful and artistic aspect of science in the form of attractors and fractals. (less)

Subject:
Mathematics
Physics
Material Type:
Activities and Labs
Instructional Material
Lesson Plans
Student Guide
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Junaid Alam
Muhammad Sabieh Anwar
Driven Diatomic Oscillator Chain Model
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Driven Diatomic Oscillator Chain Model

The Driven Diatomic Oscillator Chain model displays a one-dimensional diatomic chain of ... (more)

The Driven Diatomic Oscillator Chain model displays a one-dimensional diatomic chain of coupled harmonic oscillators with one end driven by an external force and the other end attached to a sliding rod shock absorber. The mass and Stoke's Law damping for the shock absorber are chosen to eliminate reflections at the driving frequency. The frequency of the driving force and the masses can be changed using the text boxes provided. You can change the initial position of the masses by dragging individual oscillators. You can also change the number of oscillators in the chain. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. The Driven Diatomic Oscillator Chain model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_osc_chains_OscillatorChainDrivenDiatomic.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for Newtonian mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Technology
Material Type:
Activities and Labs
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Wolfgang Christian
Duffing Chaos Model
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Duffing Chaos Model

The Ejs Duffing Chaos model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Chaos model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2 γ x' - x (1 - x²) = f cos( ω t), where each prime denotes a time derivative. The simulation displays two solutions with different initial positions and a plot of phase. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Chaos model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_chaos.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Baker’s Map Model
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Ejs Baker’s Map Model

The Ejs Baker’s Map model computes a class of generalized baker’s maps ... (more)

The Ejs Baker’s Map model computes a class of generalized baker’s maps defined in the unit square. The simulation displays the resulting points as well as the distance between adjacent points. The starting point and evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Baker’s Map model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Baker.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Attractor Model
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Ejs Duffing Attractor Model

The Ejs Duffing Attractor model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Attractor model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γ x' - x (1 - x²) = f cos(ω t), where each prime denotes a time derivative. The simulation displays a three-dimensional plot of phase space versus angle and three Poincare plots separated by angles of 2π/3. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Attractor model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_attractor.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Lecture Notes
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Baker’s Map Model
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Ejs Duffing Baker’s Map Model

The Ejs Duffing Baker’s Map model computes the solutions to the non-linear ... (more)

The Ejs Duffing Baker’s Map model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γ x' - x (1 - x²) = f cos(ω t), where each prime denotes a time derivative. The simulation displays N². Poincare plots each separated by the same phase angle. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Baker’s Map model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_Baker.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Measure Model
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Ejs Duffing Measure Model

The Ejs Duffing Measure model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Measure model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γx' - x (1 - x²) = f cos(ω t), where each prime denotes a time derivative. The simulation displays the evolution of a group of oscillators with similar initial parameters on a Poincare plot and the evolution of the oscillator with the central initial parameter displayed on a separate Poincare plot. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Measure model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_measure.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Oscillator Model
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Ejs Duffing Oscillator Model

The Ejs Duffing Oscillator model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Oscillator model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γx' - x (1 - x²) = f cos(ωt), where each prime denotes a time derivative. The simulation displays the solution as well as the phase space and Poincare plots, and energy diagram. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Oscillator model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Lecture Notes
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Phase Model
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Ejs Duffing Phase Model

The Ejs Duffing Phase model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Phase model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γx' - x (1 - x²) = f cos(ω t), where each prime denotes a time derivative. The simulation displays the evolution of a group of oscillators with similar initial parameters on a phase space plot. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Phase model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_phase.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Duffing Poincare Model
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Ejs Duffing Poincare Model

The Ejs Duffing Poincare model computes the solutions to the non-linear Duffing ... (more)

The Ejs Duffing Poincare model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2γx' - x (1 - x²) = f cos(ω t), where each prime denotes a time derivative. The simulation displays the solution Poincare plot. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Duffing Poincare model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_Poincare.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Hénon-Heiles Poincare Model
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Ejs Hénon-Heiles Poincare Model

The Ejs Hénon-Heiles Poincare model computes the solutions to the non-linear Hénon-Heiles ... (more)

The Ejs Hénon-Heiles Poincare model computes the solutions to the non-linear Hénon-Heiles Hamiltonian, which reads, ½ (pₓ² + py² + x² + y²) + x² y – 1/3 y³. The simulation displays a three-dimensional plot of phase space for the y dimension and the projection of the plane where x = 0 showing the Poincare section. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Hénon-Heiles Poincare model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Henon_Poincare.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Ejs Poincare Model
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Ejs Poincare Model

The Ejs Poincare model computes the solutions to the set of non-linear ... (more)

The Ejs Poincare model computes the solutions to the set of non-linear equations, x' = x (a - b + z + d (1-z²)) - c y, y' = y (a - b + z + d (1-z²)) + c x, z' = a z - (x² + y² + z²), where each prime denotes a time derivative. The simulation displays a three-dimensional plot of the trajectory of the oscillator and a projection on the plane where y = 0. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. Ejs Poincare model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Poincare.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Computing and Information
Physics
Material Type:
Activities and Labs
Full Course
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Fermi-Pasta-Ulam Model
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Fermi-Pasta-Ulam Model

The Fermi-Pasta-Ulam (FPU) problem is named after the numerical experiments first performed ... (more)

The Fermi-Pasta-Ulam (FPU) problem is named after the numerical experiments first performed by Enrico Fermi, John Pasta, and Stanislaw Ulam in the summer of 1953 on the Los Alamos MANIAC computer, one of the first electronic computers. They wanted to understand how a one-dimensional crystal evolves toward thermal equilibrium by simulating a chain of particles coupled by spring-like forces that included quadratic and cubic interactions. It was assumed that these nonlinear terms would cause the system to "thermalize" by redistributing energy from an initial mode into many other modes. In other words, an initial mode of vibration would quickly become more or less random. The Fermi-Pasta_Ulam model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_sto_FPU.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for statistical and thermal physics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs. (less)

Subject:
Mathematics
Physics
Material Type:
Instructional Material
Interactive
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Wolfgang Christian
Quartic Oscillator Model
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Quartic Oscillator Model

The EJS Quartic Oscillator model displays the motion of a bead moving ... (more)

The EJS Quartic Oscillator model displays the motion of a bead moving without friction along a horizontal rod, while tied to two symmetric springs. Both the motion of the masses and the phase space plot are shown in the simulation. The natural length of the springs can be changed via textboxes. (less)

Subject:
Mathematics
Science and Technology
Computing and Information
Physics
Material Type:
Full Course
Instructional Material
Interactive
Provider:
comPADRE
ComPADRE Digital Library
Provider Set:
Open Source Physics
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Spinning Hoop Model
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Spinning Hoop Model

The EJS Spinning Hoop model displays the model of a bead moving ... (more)

The EJS Spinning Hoop model displays the model of a bead moving along a hoop which is spinning about its vertical diameter with constant angular velocity ?. Friction is negligible. The simulation displays the motion of the bead as well as a plot of angle vs. time for the bead. The angular velocity of the hoop and the starting angle of the bead can be changed via sliders. (less)

Subject:
Mathematics
Science and Technology
Computing and Information
Physics
Material Type:
Instructional Material
Interactive
Provider:
comPADRE
ComPADRE Digital Library
Provider Set:
Open Source Physics
ComPADRE: Resources for Physics and Astronomy Education
Author:
Juan Aguirregabiria
Wolfgang Christian
Symmetry Breaking on a Rotating Hoop
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Symmetry Breaking on a Rotating Hoop

The Rotating Hoop Launcher package shows the dynamics of a mass that ... (more)

The Rotating Hoop Launcher package shows the dynamics of a mass that is constrained to move on a rotating hoop. The rotating hoop model is an excellent mechanical model of first- and second-order phase transitions. Although the minimum of the potential energy curve corresponds to the bottom of the hoop at low rotation frequency, a spontaneous symmetry breaking (cusp catastrophe) occurs as the frequency is increased. This package presents the theory, a demonstration, and an Easy Java Simulation (EJS) of this experiment. The package was presented at the NC Section of the AAPT Spring 2008 meeting. (less)

Subject:
Mathematics
Science and Technology
Physics
Technology
Material Type:
Instructional Material
Interactive
Provider:
comPADRE
ComPADRE Digital Library
Provider Set:
Open Source Physics
ComPADRE: Resources for Physics and Astronomy Education
Author:
Wolfgang Christian
Zeeman Catastrophe Machine Model
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Zeeman Catastrophe Machine Model

The Zeeman Catastrophe Machine Model shows the rotational motion of wheel that ... (more)

The Zeeman Catastrophe Machine Model shows the rotational motion of wheel that is free to rotate but is connected to two elastics, one which is free to move in the xy-plane, and one that is set a fixed distance d away. The model initiates in a steady state where there is no rotational velocity and the magnitude of the tensions in the two elastics are equal. The user can drag the blue point to change the torque on the wheel, or they can enter values in the input fields on the top panel. The user can also change the angle theta, the coefficient of dampening, the spring constant, the moment of inertia. The Zeeman Catastrophe Machine Model was developed as a final project in a sophomore-level Computational Physics course (Phy 200) using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item. (less)

Subject:
Mathematics
Physics
Technology
Material Type:
Instructional Material
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Andreu Glasmann
2002 llaF ,gnivloS melborP gnireenignE dna sretupmoC ot noitcudortnI

2002 llaF ,gnivloS melborP gnireenignE dna sretupmoC ot noitcudortnI

.desu si egaugnal gnimmargorp avaJ ehT .gninnalp dna ,tnemeganam ,ecneics ,gnireenigne ni ... (more)

.desu si egaugnal gnimmargorp avaJ ehT .gninnalp dna ,tnemeganam ,ecneics ,gnireenigne ni smelborp gnivlos rof seuqinhcet gnipoleved no si sisahpmE .scipot decnavda detceles dna scihparg retupmoc ,gnihcraes dna gnitros ,serutcurts atad ,sdohtem laciremun ,secafretni resu lacihparg ,stpecnoc gnimmargorp revoc smelborp gnimmargorp ylkeeW .esruoc eht fo sucof eht si tnempoleved dna ngised erawtfos detneiro-tcejbO .snoitacilppa cifitneics dna gnireenigne rof sdohtem lanoitatupmoc dna tnempoleved erawtfos latnemadnuf stneserp esruoc sihT (less)