Physical Quantities and Units Measurement of time - Pendulum lookang

« on: December 12, 2008,

version Ejs Open Source Real Pendulum Model java applet with updated features like theory period, force diagram, energy bars, drag model, reference potential energy, number of complete oscillation counter etc http://weelookang.blogspot.com/2010/06/physical-quantities-and-units.html https://dl.dropboxusercontent.com/u/44365627/lookangEJSS/export/ejs_model_Pendulumwee.jar https://dl.dropbox.com/u/44365627/lookangEJSworkspace/export/ejs_users_sgeducation_lookang_Pendulumwee.jar author: Wolfgang Christian and F. Esquembre and lookang |

Ejs Open Source Real Pendulum Model java applet |

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=818.0

Java Physics Pendulum applet modified by lookang

Physical Quantities and Units Measurement of time - Pendulum

Full screen applet

kindly hosted in NTNUJAVA Virtual Physics Laboratory by Professor Fu-Kwun Hwang

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=818.0

alternatively, go direct to http://www.phy.ntnu.edu.tw/ntnujava/index.php?board=28.0

Collaborative Community of EJS (Moderator: lookang) and register , login and download all of them for free :) This work is licensed under a Creative Commons Attribution 3.0 Singapore License

Author: Wolfgang Christian and F. Esquembre and lookang

changes:

1 was based on a much earlier version found in Ejs default examples by W. Christian and F. Esquembre

2 added alpha = d(omega)/dt = d2(theta)/dt2 into the model's visualization

3 added color scheme consistent with all my usual simulations

4 added velocity visualization

5 added context of ceiling

6 made the codes show pendulum consistently for different length L

A simple pendulum is constructed by placing a mass m at the end of a rod of length L with negligible mass. The system oscillates about the lower vertical position due to a torque τ about the pivot produced by gravity acting on the mass. Although a pendulum oscillates, the angle cannot be described by simple trigonometric functions except for small angles. Newton's Law for planar rotation states that the angular acceleration α of an object is proportional to the torque τ applied to that object

τ = I α .

The constant of proportionality I is known as the moment of inertia and can be shown to be I = mL2 for a mass that is a distance L from the point of rotation. Applying Newton's Second Law for rotation to the pendulum leads to the following second-order differential equation

d2 θ / dt2 = -(g/L) sin( θ ) .

Comparing this dynamical equation to the simple harmonic oscillator differential equation, we see that the pendulum equation undergoes simple harmonic motion for small angles when the approximation θ ~ sin( θ ) is valid. The angular frequency ω= 2πf for this small angle motion is ω= (g/L)1/2.

References:

The Simple Pendulum model is designed to teach Ejs modeling. Right click within the simulation to examine this model in the Ejs modeling and authoring tool. See:

"Modeling Physics with Easy Java Simulations" by Wolfgang Christian and Francisco Esquembre, The Physics Teacher, November 2007, 45 (Cool, pp. 475-480.

The Easy Java Simulations (EJS) manual can be downloaded from the ComPADRE Open Source Physics collection and from the Ejs website.

Note:

This simulation was created by Wolfgang Christian and Francisco Esquembre using the Easy Java Simulations (Ejs) modeling tool. You can examine and modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu. Information about Ejs is available at: .

The Pendulum model uses polar coordinates to compute the displacement angle θ but the pendulum bob in the simulation's view is positioned using Cartesian coordinates. We create x and y auxiliary variables to synchronize objects in the view with the model. These Cartesian coordinates are computed from the displacement angle when they are defined and after every animation step using an Ejs Constraints page

Because mouse actions are enabled on the bob's properties page and because the model's x and y variables are bound to the bob's x and y properties, the model's x and y variables change when the bob is dragged. This binding of on-screen properties to a model's internal variables encourages us to define a custom method newPosition that computes the displacement angle θ from the bob's Cartesian coordinates. The newPosition method also sets the bob's velocity components to zero and insures that the final coordinates are the correct distance L from the pivot point. The newPosition method is called in response to a mouse drag by entering the method name as the drag action in the bob's properties page.

The seconds pendulum, a pendulum with a period of two seconds so each swing takes one second |

If the amplitude is large like 90 degrees, the period T of a simple pendulum, the time taken for a complete cycle, is no longer approximated by |

If the amplitude is large like 45 degrees, the period T of a simple pendulum, the time taken for a complete cycle, is no longer approximated by |

If the amplitude is limited to small swings example 10 degree, the period T of a simple pendulum, the time taken for a complete cycle, is |

Wikipedia http://commons.wikimedia.org/w/index.php?title=Special:ListFiles&user=Lookang

Thumbnail | Date | Name | User | Size | Description |
---|---|---|---|---|---|

05:44, 19 August 2011 | Pendulum2secondclock.gif (file) | Lookang | 390 KB |

08:58, 26 August 2011 | Pendulum 90 degree.gif (file) | Lookang | 349 KB | ||

08:58, 26 August 2011 | Pendulum 10 degree.gif (file) | Lookang | 282 KB | ||

08:58, 26 August 2011 | Pendulum 45 degree.gif (file) | Lookang | 298 KB | ||

05:44, 19 August 2011 | Pendulum2secondclock.gif (file) | Lookang | 390 KB |

check out the other pendulums

- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1823.0 Pendulum by Francisco Esquembre (based on an original algorithm by H. Gould, J. Tobochnik, and W. Christian) Date : February 2002
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1606.0 Force analysis of a pendulum by prof Hwang modified by ahmedelshfie
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1116.0 Force analysis of a pendulum by prof Hwang
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1610.0 Pendulum (Why the angle need to be less than 5 degree --- is it necessary?) by Fu-Kwun Hwang
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=700.0 Pendulum with damping by Fu-Kwun Hwang
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1123.0 large amplitude pendulum by Fu-Kwun Hwang
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1807.0 How to combine simulation with a quicktime movie file by Fu-Kwun Hwang
- http://youtu.be/t2mhfRzwA0E Julius Sumner Miller - Physics - Pendulums pt. 1
- http://youtu.be/LOOhykNHqXM Julius Sumner Miller - Physics - Pendulums pt. 2
- http://www.compadre.org/osp/items/detail.cfm?ID=9783 Physical Pendulum Energy written by Mark Matlin
- http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html Pendulum Lab by PhET
- http://physics.bu.edu/~duffy/Ejs/EP_chapter12/pendulum_v2d.html by Andrew Duffy

1 was based on a much earlier version found in Ejs default examples by W. Christian and F. Esquembre

2 added alpha = d(omega)/dt = d2(theta)/dt2 into the model's visualization

3 added color scheme consistent with all my usual simulations

4 added velocity visualization

5 added context of ceiling

6 made the codes show pendulum consistently for different length L

26 August 2011

added special menu drop from g following Phet design http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html Pendulum Lab by PhET

added Fdrag = k*omega to simulate air resistance

added time step to allow slow down observation

add forces mg and tension add energy bars add theory pendulum Periodtheory = 2*Math.PI*Math.sqrt(L/g); from http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1610.0 Pendulum (Why the angle need to be less than 5 degree --- is it necessary?) by Fu-Kwun Hwang

add counter to calculate number of complete periods using numberofswing = Math.floor(n1/2); if(omega*omegas<0){ n1++; if(n1%2.==0.){ T1[nc]=t-ts; ts= t; } // else T1[nc]=t*2.;// first half period } omegas = omega; // to store value of omega add code to prevent program crashing

if (numberofswing>=20.) _pause(); // to prevent error in T1[100] array

add PE ref to illustrate like tracker can, the meaning of arbitrary reference level

enjoy a new and improved simulation!