## 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

## 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?

## 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

## 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 graphshttps://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMxva/SHMxva_Simulation.htmlsource: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_SHMxva.zipauthor: lookangauthor 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

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

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.