Friday, March 28, 2014

EJSS ammeter angular coil damping model

EJSS ammeter angular coil damping model, an original model by lookang
EJSS ammeter circular coil damping model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
author: lookang
author of EJSS 5.0 Francisco Esquembre

EJSS ammeter circular coil damping model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
author: lookang
author of EJSS 5.0 Francisco Esquembre



EJSS SHM model with resonance showing Amplitude vs frequency graphs, heavy damping (RED)
frequency ratio for better x azes values
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance01/SHMresonance01_Simulation.html
author: lookang
author of EJSS 5.0 Francisco Esquembre



No damping

EJSS ammeter circular coil damping model with no damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Very light damping

EJSS ammeter circular coil damping model with very light damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Light damping

EJSS ammeter circular coil damping model with light damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Moderate damping

EJSS ammeter circular coil damping model with moderate damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Critical damping

EJSS ammeter circular coil damping model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Heavy damping

EJSS ammeter circular coil damping model with heavy damping
http://weelookang.blogspot.sg/2014/03/ejss-ammeter-angular-coil-damping-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcoil/SHMcoil_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMcoil.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Wikipedia

http://upload.wikimedia.org/wikipedia/commons/9/9c/Ampere-o-meter-vintage-HDR-0h.jpg

my edited version:



YJC note

2) Moving-coil meters
Critical damping is an important feature of moving-coil meters which are used to measure current and voltage. When the reading changes, it is of little use if the pointer oscillates for a while or takes too long to settle down to the new reading. The new reading must be taken quickly in case it changes again.
Thus, a pointer is critically damped to allow it to move to the correct position immediately whenever a current flows through it or a voltage is applied across it.

The equations that model the motion of the car suspension spring mass system are:

Mathematically, the restoring force $ F $ is given by 

$ F = - k (\theta - \theta_{0}) $

where $ F $  is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and $ \theta $ is the displacement from the equilibrium position $ \theta_{0} $ (in radians).

Thus, this model assumes the following ordinary differential equations:

$ \frac{\delta \theta }{\delta t} = \omega $


$ \frac{\delta \omega }{\delta t} = -\frac{k}{m} (\theta - \theta_{0})  - b\frac{\omega}{m} +  $

where the terms

$ -\frac{k}{m} (\theta - \theta_{0}) $ represents the restoring force component as a result of the coil spring extending and compressing.

$ - b\frac{\omega}{m}$ represents the damping force component as a result of dampers retarding the car mass's motion.



Thursday, March 27, 2014

2014 PS21 Star Service Award Winner

news is out! 2014 PS21 Star Service Award Winner. #edsg
16 colleagues from MOE and MOE Statutory Boards will be awarded the PS21 Star Service Award (2014). write up to support my nomination is here.

Congratulations go to the following 2014 PS21 Star Service Awardees [PSSSA] (not arranged in any order of merit):


1
Leong-Ho Hil May
MOE HQ
Education Services Division
2
Wee Loo Kang Lawrence
MOE HQ
Educational Technology Division
3
Arthur Poh
MOE HQ
Higher Education Division
4
Noor Huda Abu Samah
MOE HQ
School Planning and Placement Division
5
Vikneswaran s/o Krishnan Murthi
MOE School
Anglo-Chinese School (Barker Road)
6
Yang Su Yin
MOE School
Gan Eng Seng Primary School
7
Liau Thiam Huat
MOE School
Henderson Secondary School
8
Denise Teh Shu Hui
MOE School
Junyuan Secondary School
9
Vicknesh Thiagarah
MOE School
Mayflower Secondary School
10
Karlinah Binte Sahadan
MOE School
Pei Tong Primary School
11
Nur Hidayah Binte Eser
MOE School
Serangoon Garden Secondary School
12
Choo Kok Luang
MOE School
Si Ling Secondary School
13
Lee Kim Seng
MOE School
St. Hilda’s Secondary School
14
Lee Thiam Hin Ivan
MOE School
Zhonghua Secondary School
15
Hanley Loo
MOE Statutory Board
Institute of Technical Education (ITE College East)
16
Tan Ai Chin
MOE Statutory Board
Republic Polytechnic


1) Videoshoot

Date: 2 Apr 2014
Venue:  Bishan Public Library (located behind Junction 8) 5 Bishan Place, #01-01 Singapore 579841. Programme Zone at Level 2 How to get there: Link
Time: 10am - 1pm

2) Photoshoot (not required if i am attending 1) 

Date: 15 Apr 2014
thanks to winston tan for the photo!








Venue: Multi-Purpose Room, Central Public Library, (located at the National Library Building, 100 Victoria Street, Basement 1, Singapore 188064.) How to get there: Link
Time: 10am - 11am
Questions:
  1. Describe one quality needed in your work and why
    1. Quality needed is the ability stay focused and true to vision of the Public Service. 
    • v2 actual used: Technology - Using Educational Technology to allow students to be interactively engagement thereby bringing out the best in every child. 
    • v1: There are many initiatives (21CC, mp3, teach less, learn more) and frameworks (cyberwellness, 21CC, C2015) being rolled out in my Ministry that require us to rationale and make sense, perhaps even make more vivid and better than the original localized intent. The world is already so connected through the internet, why not push our initiatives and frameworks to benefit young children in developing as well as other industrialized countries? If by spending 1 dollar more can make millions of children everywhere learn better through the internet, I say just do it because it is what public service is about, for the benefit of the general public.  
  2. In a few sentences, describe one definitive moment in your line of work
    1. To experience the joy of students having evidence based discussions and having them to tell their perspectives on how we can improve the learning and teaching practices. There is always something to improve on and the feedback fuels my service and work.
    2. I also recently created a suite of TEN mobile devices enabled simulations and i emailed Physics teachers in almost all the junior colleges, and some of them replied back about how the were able to incorporate them into their existing teaching and practices, just make me happy. Some of the teachers even suggested ways to customized the simulations to better suit their practices, that really is a rewarding experience knowing that busy teachers find value in the work and service that i provide.
  3. In a few sentences, describe the person who inspired you
    1. Professor Hwang Fu-Kwun from Taiwan, Professor Francisco Esquembre from Spain and Professor Wolfgang Christian, USA are the 3 people's work and passion have inspired me to give away free and open sourced thousands of educational resources so that these simulations can be changed legally under the licenses of creative commons attributions and other compatible licenses like GNU. They are truly role models for me as they selflessly give their intellectual creations away for the benefit of all humankind, that the reason, I am who I am today, able to serve selflessly for public good. 
  4. In a few sentences, give one way to encourage Singaporeans to pursue public service
    1. Once you can figure out 'why' you should be in the business of public service such as Ministry of Education like I have, you will be able to act beyond and do further then what is articulated and set yourself to achieve more lasting change for the benefit of all others, before self. 

3) Submission of self-taken photograph (not required since i am attending 1) and 2)

If you are unable to meet the time for the photoshoot, you may submit your self-taken photograph to us.
In order for the photo to come up well, the requirements are as follows:
  1. At least 300dpi: portrait style – upper body only; from the buttocks up (photo should not show the legs)
  2. JPEG format
  3. Should not be candid photo but professional-looking (see attached examples provided)
  4. Those serving public in uniform should be in full uniform
  5. Person should not fill up whole photo; there should be some space at the top, bottom and sides (about 2-3cm) - file size should be at least 1MB
  6. Should be brightly lit – not taken in dark places.

4) Write-up for commemorative e-publication

We need a short write-up from you for our e-publication.
Please provide a paragraph or two (not more than 80 words) that answers any ONE of the following questions :
  1. What motivates you to serve/continue in your work?
    1. v2: 1. Make the world a better place for everyone. Just doing my humble part as an concerned citizen of the world by contributing to open educational resources, creating engaging and interactive computer models-simulations that support active learning for improving education all over the world. Thus my motivation is to serve students, teachers and the public with the well designed and customized simulations resources for the world, while being rooted in Singapore.
    2. v1: Make the world a better place for everyone. Just doing my humble part as an concerned citizen of the world by contributing to open educational resources, creating engaging and interactive computer models-simulations that support self directed and personalized active learning for improving education all over the world, granting universal access to quality resources. This my motivation to serve students, teachers and the public with the well designed and customized simulations resources.  
  2. How do you deal with difficult situations/customers?
  3. Can you describe a memorable event in your working life/made an impact on another individual or something that left a deep impression on you.
  4. One tip/advice for others to provide excellent service.
  5. Any other thing you want to share?



2013 PS21 Distinguished Star Service Award Winner - Brinda Naid


 

Wednesday, March 26, 2014

EJSS car suspension model

EJSS car suspension model, an original model by lookang
EJSS car suspension model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre
EJSS car suspension model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre


EJSS SHM model with resonance showing Amplitude vs frequency graphs, heavy damping (RED)
frequency ratio for better x azes values
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance01/SHMresonance01_Simulation.html
author: lookang
author of EJSS 5.0 Francisco Esquembre



No damping

EJSS car suspension model with no damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Very light damping

EJSS car suspension model with very light damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre


Light damping

EJSS car suspension model with light damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Moderate damping

EJSS car suspension model with moderate damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Critical damping

EJSS car suspension model with critical damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Heavy damping

EJSS car suspension model with heavy damping
http://weelookang.blogspot.sg/2014/03/ejss-car-suspension-model.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxvaverticalcar/SHMxvaverticalcar_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxvaverticalcar.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Wikipedia

https://en.wikipedia.org/wiki/Suspension_(vehicle) A rear independent suspension on an AWD car


YJC note

13.3.2 Applications of Critical Damping
1) Car suspension
The spring of a car’s suspension is critically damped so that when a car goes over a bump, the passenger in the car quickly and smoothly regains equilibrium.
However, car suspensions are often adjusted to slightly under-critically damped condition to give a more comfortable ride. Critical damping also leaves the car ready to respond to further bumps in the road quickly.

The equations that model the motion of the car suspension spring mass system are:

Mathematically, the restoring force $ F $ is given by 

$ F = - k y $

where $ F $  is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and y is the displacement from the equilibrium position (in m).

Thus, this model assumes the following ordinary differential equations:

$ \frac{\delta x}{\delta t} = v_{y} $


$ \frac{\delta v_{y}[i]}{\delta t} = -\frac{k}{m}(y) - \frac{bv_{y}}{m} + \frac{A sin(2 \pi f t)}{m} $

where the terms

$ -\frac{k}{m}(y) $ represents the restoring force component as a result of the spring extending and compressing.

$ - \frac{bv_{y}}{m}$ represents the damping force component as a result of dampers retarding the car mass's motion.

$ + \frac{A sin(2 \pi f[i] t)}{m} $ represents the driving force component as a result of a external periodic force acting the mass $ m $ for example from the road.

Forced oscillations

Forced oscillations are oscillations that are subjected to a periodic driving force provided by an external agent such as motor or a push by a person etc.

Resonance is an interesting phenomenon that occurs when driving force frequency matches that of the system's natural oscillating frequency resulting in a motion that reaches some maximum amplitude.

Resonance

In physics, resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. At these frequencies, even small periodic driving forces $ + \frac{A sin(2 \pi f t)}{m} $ can produce large amplitude oscillations, because the system stores vibrational energy.

Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a spring mass system). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.



Monday, March 24, 2014

EJSS SHM model with resonance showing Amplitude vs frequency graphs

EJSS SHM model with resonance showing Amplitude vs frequency graphs 
EJSS simple harmonic motion model with Amplitude vs frequency graphs
based on models and ideas by
EJSS SHM model with resonance showing Amplitude vs frequency graphs, heavy damping (RED)
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance01/SHMresonance01_Simulation.html
author: lookang
author of EJSS 5.0 Francisco Esquembre
EJSS SHM model with resonance showing Amplitude vs frequency graphs, heavy damping (RED)
frequency ratio for better x azes values
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance01/SHMresonance01_Simulation.html
author: lookang
author of EJSS 5.0 Francisco Esquembre

  1. lookang http://weelookang.blogspot.sg/2014/03/ejs-resonance-frequency-vs-amplitude.html
  2. Wolfgang Christian EJS examples by wolfgang, such as\source\users\davidson\wochristian\osc\SHOResonance.xml


No damping

EJSS SHM model with resonance showing Amplitude vs frequency graphs, no damping
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre


Very light damping

EJSS SHM model with resonance showing Amplitude vs frequency graphs, very light damping (RED)
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre


Light damping


EJSS SHM model with resonance showing Amplitude vs frequency graphs, light damping (RED)
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Moderate damping

EJSS SHM model with resonance showing Amplitude vs frequency graphs, moderate damping (RED)
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Critical damping

EJSS SHM model with resonance showing Amplitude vs frequency graphs, critical damping (RED)
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Heavy damping

EJSS SHM model with resonance showing Amplitude vs frequency graphs, heavy damping (RED)
http://weelookang.blogspot.com/2014/03/ejss-shm-model-with-resonance-showing.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMresonance/SHMresonance_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMresonance.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre

Wikipedia

https://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Resonance.PNG/1200px-Resonance.PNG


YJC note

yjc notes

The equations that model the motion of the many spring mass system are:

Mathematically, the restoring force $ F[i] $ is given by 

$ F[i] = - k x[i] $

where $ F[i] $  is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and x[i] is the displacement from the equilibrium position (in m).

Thus, this model assumes an array of object in [i] dimensional where number of objects is n = 50

$ \frac{\delta x[i]}{\delta t} = v_{x}[i] $


$ \frac{\delta v_{x}[i]}{\delta t} = -\frac{k}{m}(x[i]-l) - \frac{bv_{x}[i]}{m} + \frac{A sin(2 \pi f[i] t)}{m} $

where the terms

$ -\frac{k}{m}(x[i]-l) $ represents the restoring force component as a result of the spring extending and compressing.

$ - \frac{bv_{x}[i]}{m}$ represents the damping force component as a result of drag retarding the mass's motion.

$ + \frac{A sin(2 \pi f[i] t)}{m} $ represents the driving force component as a result of a external periodic force acting the mass $ m $.

Forced oscillations

Forced oscillations are oscillations that are subjected to a periodic driving force provided by an external agent such as motor or a push by a person etc.

Resonance is an interesting phenomenon that occurs when driving force frequency matches that of the system's natural oscillating frequency resulting in a motion that reaches some maximum amplitude.

Resonance

In physics, resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. At these frequencies, even small periodic driving forces $ + \frac{A sin(2 \pi f[i] t)}{m} $ can produce large amplitude oscillations, because the system stores vibrational energy.

Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a spring mass system). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.


Thursday, March 20, 2014

EJS Resonance Frequency vs Amplitude Curve Model

EJS Resonance Frequency vs Amplitude Curve Model by Wolfgang and lookang.

based on a conversation 2008 here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=821.0
the original can be found in EJS examples by wolfgang, such as \source\users\davidson\wochristian\osc\SHOResonance.xml

EJS Resonance Frequency vs Amplitude Curve Model by Wolfgang and lookang.
http://weelookang.blogspot.sg/2014/03/ejs-resonance-frequency-vs-amplitude.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejs_model_SHOResonancewee.jar
author: Wolfgang and lookang

Contextualization of spring mass system:

refer to another model here
EJSS simple harmonic motion model with x vs t, v vs t and a vs t graphs
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxva/SHMxva_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxva.zip
author: lookang
author of EJSS 5.0 Francisco Esquembre


Physics Model of spring mass system with amplitude vs driving frequency graph showing the concept of resonance :

The following ordinary differential equations are used:

$ \frac{\delta x}{\delta t} = v $

$ \frac{\delta v}{\delta t} = -\frac{k}{m}x -\frac {b}{m}v + \frac{A cos( \omega t)}{m} $

where
$ -\frac{k}{m}x $ is the restoring acceleration component from simple harmonic motion

$ -\frac {b}{m}v $ is the damping acceleration as a result of the viscous fluid the spring mass system in experiencing

$ +\frac{A cos( \omega t)}{m} $ is the driving acceleration component due to an external driving force agent.

The key to determining the maximum amplitude is from the energy equation

since


$ TE= \frac{1}{2}mv^{2} +  \frac{1}{2}kx^{2}$


it can be shown that the various maximum amplitudes happens at $ v = 0 $, thus,

$ X_{max}= \sqrt{\frac{2TE}{k}}$

by stepping through 50 transientCounter, the $ X_{max} $ can be determined and plotted by plotting by $ \delta f $, the corresponding $ X_{max} $ can be found. 

The equation is used to determine the natural frequency and natural angular velocity of the spring mas system

$ f_{o}=\frac{1}{2} \pi \sqrt \frac{k}{m} $

$ \omega_{o}= \sqrt \frac{k}{m} $


Levels of damping

the following assumption are made for modeling the damping factor 

$ \tau = \frac{b}{2 \sqrt{mk}}$

very_light_damping when $ \tau = 0.05$
very_light_damping when $ \tau = 0.05$


light_damping when $ \tau = 0.1$
light_damping when $ \tau = 0.1$


moderate_damping when $ \tau = 0.2 $
moderate_damping when $ \tau = 0.2 $



critical_damping when $ \tau = 1.0$
critical_damping when $ \tau = 1.0$


heavy_damping when $ \tau = 2.5$
heavy_damping when $ \tau = 2.5$


for the corresponding damping coefficient  $ b $ values to show correctly, the equation is use

$ b = 2 \sqrt{mk} \tau $

Changes made by lookang


  1. added dropdrop menu with ease of learning thanks to fu-kwun many examples
  2. added dotted line for visualization of natural frequency $ f_{o} $ thanks to paco for sharing how
  3. modified the trail instead of trace for color change thanks to paco
  4. modified the existing object oriented programming style to draw thank to wolfgang
  5. added pause when $ f >= 2f_{o}$ for plotting 2 twices the x size consistently
  6. layout to my usual design
  7. added m and k for contextualization of the spring mass system


Physics i don't understand


strangely which a different driving force component, the graph can show maximum curve characteristics but it starts at (0,0) instead of (0,A).


start at (0,A) which i am not is correct, but has maximum curve characteristics (which i believe is correct)


$ +\frac{A sin( \omega t)}{m} $ is the driving acceleration component due to an external driving force agent.