### 11.4 Oscillators and Pendulums

15. Inertial Oscillation Model

*.jar The EJS Inertial Oscillation model displays the motion of a particle moving over the surface of an oblate spheroid. The spheroid is flattened to an ellipsoid of revolution because it is rotating, just as the ...

17. Foucault Pendulum Model

*.jar The EJS Foucault Pendulum model displays the dynamics of a Foucault pendulum. The simulation is designed to show the dynamical explanation of why precession of the Foucault pendulum is slower at lower latitudes. ...

18. Circumnavigating Pendulum Model

*.jar The EJS Circumnavigating Pendulum model displays the dynamics of a mechanical oscillator in uniform circular motion. The mechanical oscillator is free to move in two directions. This 2-dimensional simulation ...

34. Strange Harmonic Oscillator Model

*.jar The EJS Strange Harmonic Oscillator model displays the motion of two masses connected by a massless rigid rod, and the masses may move without friction along two perpendicular rails in a horizontal table. ...

35. Quartic Oscillator Model

*.jar 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 ...

36. Damped Driven Harmonic Oscillator Phasor Model

*.jar The EJS Damped Driven Harmonic Oscillator Phasor model displays the motion of damped driven harmonic oscillator. The resulting differential equation can be extended into the complex plane, and the resulting ...

38. Spring Pendulum Model

*.jar The EJS Spring Pendulum model displays the model of a hollow mass that moves along a rigid rod that is also connected to a spring. The mass, therefore, undergoes a combination of spring and pendulum oscillations. ...

39. Oscillator Chain Model

*.jar The EJS Oscillator Chain model shows a one-dimensional linear array of coupled harmonic oscillators with fixed ends. This model can be used to study the propagation of waves in a continuous medium and the ...

45. Pendulum on an Accelerating Train Model

*.jar The EJS Pendulum on an Accelerating Train model displays the model of a pendulum on an accelerating train. The problem assumes that the pendulum rod is rigid and mass-less and of length L = 2, and the pendulum ...

50. Coupled Oscillators and Normal Modes Model

*.jar The EJS Coupled Oscillators and Normal Modes model displays the motion of coupled oscillators, two masses connected by three springs. The initial position of the two masses, the spring constant of the three ...

51. Spinning Hoop Model

*.jar 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 ...

56. Anisotropic Oscillator Model

*.jar The EJS Anisotropic Oscillator model displays the dynamics of a mass connected to two opposing springs. The simulation displays the motion of the mass as well as the trajectory plot. The initial position ...

58. Oscillations and Lissajous Figures Model

*.jar The EJS Oscillations and Lissajous Figures model displays the motion of a superposition of two perpendicular harmonic oscillators. The simulation shows the result of the superposition. The amplitude and ...

73. Action for the Harmonic Oscillator Model

*.jar The EJS Action for the Harmonic Oscillator model displays the trajectory of a simple harmonic oscillator by minimizing the classical action. The simulation displays the endpoints of the motion (t,x) which ...

#### 11.4.1 Quantum Mechanics

27. Circular Well Superposition Model

*.jar The Circular Well Superposition simulation displays the time evolution of the position-space wave function in an infinite 2D circular well. The default configuration shows the first excited state with zero ...

49. QM Eigenstate Superposition Demo Model

*.jar The EJS QM Eigenstate Superposition Demo model displays the time dependence of a variety of superpositions of energy eigenfunctions for the infinite square well and harmonic oscillator potentials. One of ...

54. Barrier Scattering model

*.jar The EJS Barrier Scattering model shows a quantum mechanical experiment in which an incident wave (particle) traveling from the left is transmitted and reflected from a potential step at x=0. Although ...

59. Free Particle Eigenstates

*.jar The free particle energy eigenstates model shows the time evolution of a superposition of free particle energy eigenstates. A table shows the energy, momentum, and amplitude of each eigenstate.

61. Eigenstate Superposition

*.jar The fundamental building blocks of one-dimensional quantum mechanics are energy eigenfunctions Psi(x) and energy eigenvalues E. The user enters the expansion coefficients into a table and the simulation ...

74. Wave Packet Model

*.jar The EJS Wave Packet model displays the motion of an approximate wave packet. The simulation allows an arbitrarily wave packet to be created. The default dispersion relation, with the frequency equal to the ...

#### 11.4.2 Theory of of Relativity

65. Einstein’s Train and Tunnel Model

*.jar The EJS Einstein Train and Tunnel model displays the famous thought experiment from special relativity where a train enters a tunnel as seen from two points of view. In one case the train is seen in the ...

66. Simultaneity Model

*.jar The EJS Simultaneity model displays the effect of relative motion on the relative ordering of the detection of events. The wave source and two equidistant detectors are at rest in reference frame S’, which ...

#### 11.4.3 Statistics

4. Random Walk 2D Model

*.jar The EJS Random Walk 2D Model simulates a 2-D random walk. You can change the number of walkers and the probability of going a given direction. You can modify this simulation if you have EJS installed by right-clicking ...

5. Random Walk 1D Continuous Model

*.jar The EJS Random Walk 1D Continuous Model simulates a 1-D random walk with a variable step size. You can change the number of walkers and the probability of going right and left. You can modify this simulation if ...

29. Balls in a Box Model

*.jar The Balls in a Box model shows that a system of particles is very sensitive to its initial conditions. In general, an isolated system of many particles that is prepared in a nonrandom configuration will change ...

32. Multiple Coin Toss Model

*.jar The EJS Multiple Coin Toss model displays the result of the flipping of N coins. The result of each set of coin flips is shown by the image of the pennies on the screen and the complete results of the tossing ...

#### 11.4.4 Thermodynamics

10. Kac Model

*.jar The EJS Kac Model simulates the relaxation of a gas to equilibrium by randomly selecting and then colliding gas molecules but without keeping track of the molecules’ positions. As long as the collisions are ...

12. 2D-Ising Model

*.jar The EJS 2D-Ising model displays a lattice of spins. You can change the lattice size, temperature, and external magnetic field. You can modify this simulation if you have EJS installed by right-clicking within ...

#### 11.4.5 Waves

52. Beats Model

*.jar The EJS Beats model displays the result of adding two waves with different frequencies. The simulation displays the superposition of the two waves as well as a phasor diagram that shows how the waves add ...

57. Normal Modes on a Loaded String Model

*.jar The EJS Normal Modes on a Loaded String model displays the motion of a light string under tension between two fixed points. The string is also loaded with N masses located at regular intervals. The number ...

63. Doppler Effect Model

*.jar The EJS Doppler Effect model displays the detection of sound waves from a moving source and the change in frequency of the detected wave via the Doppler effect. In addition to the wave fronts from the source ...

75. Waveguide Model

*.jar The EJS Waveguide model displays the motion of a traveling wave forced to move between two walls in a waveguide. The two walls are located at $Math content$ and $Math content$, so that its normal modes are $Math content$

76. Waves and Phasors Model

*.jar The EJS Waves and Phasors model displays the motion of a transverse wave on a string and the resulting phasors for the wave amplitude. The simulation allows an arbitrarily polarized wave to be created. The ...

77. Transverse Wave Model

*.jar The EJS Transverse Wave model displays the motion of a transverse wave on a string. The simulation allows an arbitrarily polarized wave to be created. The magnitude of the components of the wave and the ...

79. Reflection and Refraction between Taut Strings Model

*.jar The EJS Reflection and Refraction between Taut Strings model displays the motion of a traveling pulse on a string when it is incident on a change of string density. ...

80. Standing Waves on a String Model

*.jar The EJS Standing Waves on a String model displays the motion of a standing wave on a string. The standing wave can be augmented by adding the zero line and the maximum displacement of the string. The number ...

81. Resonance in a Driven String Model

*.jar The EJS Resonance in a Driven String model displays the displacement of taut string with its right end fixed while the left end is driven sinusoidally. The driving frequency, amplitude, and the simulation’s ...

82. Standing Waves in a Pipe Model

*.jar The EJS Standing Waves in a Pipe model displays the displacement and pressure waves for a standing wave in a pipe. The pipe can be closed on both ends, on one end, or open on both ends. The number of nodes ...

84. Group Velocity Model

*.jar The EJS Group Velocity model displays the time evolution for the superposition of two traveling waves of similar wave numbers and frequencies. The simulation allows an arbitrarily superposition of two waves ...

#### 11.4.6 Miscellaneous

*.jar The EJS Radioactive Decay Events Model simulates the decay of a radioactive sample using discrete random events. It displays the number of events (radioactive decays) as a function of time in a given time ...

*.jar The EJS Radioactive Decay Distribution Model simulates the decay of a radioactive sample using discrete random events. It displays the distribution of the number of events (radioactive decays) in a fixed time ...

19. Game of Life Model

*.jar The EJS Game of Life Model simulates a popular 2D cellular automaton of a lattice in a finite state which is updated in accordance with a set of nearby-neighbor rules. The universe of the Game of Life, developed ...

*.jar The EJS Radioactive Decay Model simulates the decay of a radioactive sample using discrete random events. It displays the number of radioactive nuclei as a function of time. You can change the initial number ...

A large number of older EJS-examples, among them very elementary ones, is found in the users directory that belong to the directory tree of this work. The can also be downloaded with the EJS console from the EJS console. In the users directory the files are ordered after the authors. There are .xlm files in this directory, that are not executable by themselves and have to be loaded by the EJS console. The following figure 11.7 of the directory tree will facilitate the orientation.

The directories of the authors are located below the directory source/users. In Fig.11.7 the directory tree details the sub-directory of Francisco Esquembre:Murcia/Fem (University of Murcia, Spain).

In order to enable the user to get an overview over the large number of these simulations, the directory export contains in its sub-directory Others/EJS directly runnable *.jar files of the simulations next to the corresponding *.xml files (see Fig.11.8).

With the hyperlink on the margin next Fig.11.9 one reaches an overview file, that contains information about 144 simulations ordered according to 16 topics, supplemented with short comments and a reference for the respective source. The individual simulations can be called quickly and directly via clicking on the file name.

The files are of very different complexity. In addition to a few child-friendly simulations there are simple example for the demonstration of certain visualization possibilities. The majority of the files contains quite complex simulations of physical problems, with optical visualizations that are in a number of cases quite convincing. Some of the simulations can also be found under the new individual files, that were discussed at the beginning of the chapter. Some of these have been developed further.

Many of the files contain no description pages. Testing which elements of the graphics can be pulled with the mouse often reveals initially unexpected design possibilities.

The files can be edited and further developed, if the corresponding *.xml file is called from the EJS console.