NTNUJAVA Virtual Physics Laboratory
Enjoy the fun of physics with simulations!
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Author Topic: Pendulum  (Read 384674 times)
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Fu-Kwun Hwang
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on: January 29, 2004, 05:35:38 pm » posted from:,,Satellite Provider

Registed user can get files related to this applet for offline access.
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You are welcomed to check out Force analysis of a pendulum


How to change parameters?
    Set the initial position
    Click and drag the left mouse button
      The horizontal position of the pendulum will follow the mouse Animation starts when you release the mouse button

  1. Adjust the length

  2.  dragging the pointer (while > holding down the left button)
      from the support-point (red dot) to a position that sets the length you want.

    Animation starts when you release the mouse button
  3. Change gravity g

  4.  Click near the tip of the red arrow,
      and drag the mouse button to change it (up-down).

  5. Change the mass of the bob

  6.  Click near the buttom of the black stick,
      and drag the mouse button to change it (up-down).


Information displayed:
    1. red dots: kinetic energy K = m v*v /2 of the bob 2. blue dots: potential energy U = m g hof the bob
    Try ro find out the relation between kinetic energy and pontential energy! 3.black dots (pair) represent the peroid T of the pendulum
      move the mouse to the dot :
        will display information for that dot in the textfield


Click show checkbox to show more information
    blue arrow(1): gravity green arrows(2): components of gravity red arrow
    (1): velocity of the bob
    Try to compare velocity and the tangential component of the gravitional force!


The calculation is in real time (use Runge-Kutta 4th order method). The period(T) is calculated when the velocity change direction.
    You can produce a period verses angle ( T - X ) curve on the screen,just started at different positions and wait for a few second.


Therotically, the period of a pendulum T=\sqrt{g/L}.
Purpose for this applet:
1. The period of the pendulum mostly depends on the length of the pendulum and the gravity (which is normally a constant)
2. The period of the pendulum is independent of the mass.
3. The variation of the pendulum due to initial angle is very small.

The equation of motion for a pendulum is \frac{d^2\theta}{dt^2}=-\frac{g}{L}\, \sin\theta
when the angle is small \theta << 1 ,\sin\theta\approx \theta
so the above equation become \frac{d^2\theta}{dt^2}\approx-\frac{g}{L}\, \theta
which imply it is approximately a simple harmonic motion with period T=2\pi \sqrt{\frac{L}{g}}

What is the error introduced in the above approximation?
From Tayler's expansion \sin\theta=\theta-\frac{\theta^3}{3!}+\frac{\theta^5}{5!}-\frac{\theta^7}{7!}+\frac{\theta^9}{9!}-\frac{\theta^11}{11!}+...
To get first order approximation, the error is \frac{\theta^3}{3!}=\frac{\theta^3}{6}
So the relative error (error in percentage)= \frac{\theta^3/6}{\theta}=\frac{\theta^2}{6}
If the angle is 5 degree, which mean \theta=5*pi/180\approx=5/60=1/12
So the relative error is \frac{\theta^2}{6}=1/(12^2*6)=1/(144*6)=1/864\approx 0.00116

For angle=5 degree , the relative error is less than 0.116%
For angle=10 degree , the relative error is less than 0.463%
For angle=20 degree , the relative error is less than 1.85%

So the period of the pendulum is almost independent of the initial angle (the error is relatively small unless the angle is much larger than 20 degree- for more than 2% error).


Registed user can get files related to this applet for offline access.
Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
If java program did not show up, please download and install latest Java RUN TIME
There are 18 translations,
Higher number at the end means more translation been done.
or


*** There are 1 more attached files. You need to login to acces it!
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Reply #1 on: January 30, 2004, 11:24:21 am » posted from:,,Satellite Provider

Subject: Thanks
Date: Wed, 9 Dec 1998 16:07:30 -0500
From: louise heaven <gw_heaven@compuserve.com>
To: Fu-Kwan Hwang <hwang@phy03.phy.ntnu.edu.tw>
Thank you very much Mr Hwang, for your reply to my plea about the pendulum.
 I was very pleasently surprized to find you had done so. Thankyou again.
I would also like to say that you have a very good web page and i shall
look there first when i am researching physics.

Joseph Heaven
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Reply #2 on: January 30, 2004, 04:39:57 pm » posted from:Taipei,T'ai-pei,Taiwan

From: Bill Kinsella <wkinsella@csi.com>
Reply-To: "wkinsella@csi.com" <wkinsella@csi.com>
To: "'hwang@phy03.phy.ntnu.edu.tw'" <hwang@phy03.phy.ntnu.edu.tw>
Subject: Java Applets
Date: Sat, 6 Nov 1999 21:04:16 -0000

Dear Sir,

I came across your site when I was searching for material for my son who is
studying science and in particular the pendulum. I was facinated by the
immediacy and effficacy of the applets. Surely this must represent a major
advancement in the teaching of physics as well as being great fun.

Unlike you I spent most of may life as a software developer although I know
nothing of Java type languages and now work as a power company nework
controller an can think of many interactive applications for our intranet.

I would like to see an applet developed illustrating the principles of
simple roof truss design.

Thanks for the enjoyment your work provided,

Bill Kinsella
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Reply #3 on: March 22, 2004, 01:55:17 pm »

From what I learned in physics. The equation for the period of a simple pendulum is T=2(pi)(L/G)^1/2. Which means constant length should result in constant period. However I change the angle of release on the pendulum and the period changes!!??.
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ratznium
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Reply #4 on: February 07, 2005, 10:49:45 pm »

There's must be an energy leak somewhere in the system. Instead of it's simulated perpetual motion, the bob eventually increases speed so that it ends up going right around a full circle, above the top of the java applet.


It's happened twice in a row now as I've left the applet running in the background while going through physics questions.

Try it out yourself if you're interested. Leave the applet running for at least an hour, and it ought to go wild.
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Fu-Kwun Hwang
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Reply #5 on: February 12, 2005, 01:57:17 pm »

For the computer simulation, there is always some error due to calculation.
Yes. it will happened when running the simulation for a long time.
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Fu-Kwun Hwang
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Reply #6 on: February 12, 2005, 02:07:43 pm »

[quote:0748e969ef="Anonymous"]From what I learned in physics. The equation for the period of a simple pendulum is T=2(pi)(L/G)^1/2. Which means constant length should result in constant period. However I change the angle of release on the pendulum and the period changes!!??.[/quote:0748e969ef]

The period of the pendulum is almost constant if the amplitude if small (small angle vibration)
However, the period will change very small amount when the angle increase.
It only increase less than 2% for 20 degree (relative to vertical line).
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rhipple
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Reply #7 on: April 24, 2006, 07:18:06 am »

I would like to execute this applet offline. This feature appears to be disabled at the current time. This post will serve as my notification when to try again.
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rhipple
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Reply #8 on: April 25, 2006, 09:22:51 am »

Great! I have a local version of the applet. Now may I see the source? I would like to tinker with it.
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Reply #9 on: March 09, 2007, 07:28:55 pm »

Hi there, I was very excited to find the pendulum simulation, but I am trying to measure differences with different lengths, then with the same length and different masses at the end of the pendulum and I cant seem to change the mass without it disappearing off the end of my screen! I am obviously doing something wrong.  I would like to simulate a length of 30cm with masses of 100,200,300,400,500 grams, is this realistic?  I want the angle to be 45 degrees - would be grateful if you could help me to do this.  Thanks and regards Mary
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Fu-Kwun Hwang
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Reply #10 on: March 09, 2007, 11:31:09 pm »

If you want to set the length and angle of the pendulum, move your mouse to the red dot at the center on the top of the simulation, click down the mouse and drag the mouse away. The textfield on the top will display length and angle of the pendulum. When you are done just release the mouse.
If you want to change mass of the object, drag the vertical line (label with mass) up and down to change  mass.
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DKMFan
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Reply #11 on: June 03, 2007, 08:12:26 pm »

Wow. I like. A lot.

Do you mind if I use that for my coursework? It involves making a pendulum have the time period to be used for a Grandfather Clock. I'm asking in case something shows up in the mark scheme which means I'll have to eventually.

Quote from: link=topic=11.msg68#msg68 date=1079938517
From what I learned in physics. The equation for the period of a simple pendulum is T=2(pi)(L/G)^1/2. Which means constant length should result in constant period. However I change the angle of release on the pendulum and the period changes!!??.

And thank you for making it a lot easier to find the equation. I think I needed that for my homework. Hmmm.
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Fu-Kwun Hwang
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Reply #12 on: June 04, 2007, 10:12:53 pm »

You are welcomed to use it for your coursework.

The equation T=2(pi)(L/G)^1/2 is good only for small angle.
(The sinθ was replaced by θ when derive the equation)
It will be a little different when the angle is larger.
However, the difference is usually very small.
So it is still a very good approximation unless you need very high resolution results.
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green
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Reply #13 on: February 25, 2008, 10:52:20 am » posted from:Jakarta,Jakarta Raya,Indonesia

i have download it, but i still can not find the source code. can u help me??
how can i get all of your source code from this site??
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Fu-Kwun Hwang
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Reply #14 on: February 25, 2008, 11:24:38 am » posted from:Taipei,T\'ai-pei,Taiwan

EJS Source code are available for all the simulations created with EJS, i.e.
 Simulations under category [ Easy Java Simulations (2001- ) ]

For applets created with JDK1.0.2 (I created those between 1996-2001), source code are only included with very few download ZIP files.  I did  not add source code in the ZIP files, because most of the user did not need it. And those (including pendulum applet shown in this topic) are all created with JDK1.0.2
However, I just sent the source code to your email. You might need to change some of the code if you want to compile those code with current version JDK.
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Reply #15 on: May 23, 2008, 02:08:09 pm » posted from:Zrenjanin,Vojvodina,Serbia

Please help me, I need with pendulum to determinate earth acceleration.
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Reply #16 on: May 30, 2008, 01:23:22 pm » posted from:Zrenjanin,Vojvodina,Serbia

This pendulum is great, only it won't stop. I need to measure earth acceleration with equation t=N/T and g=4*PI (2*(L/100)/t^2). Somebody please help me!
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Reply #17 on: May 30, 2008, 03:03:53 pm » posted from:Taipei,T\'ai-pei,Taiwan

It will toggle between pause/play if you RIGHT CLICK mouse button inside the simulation region.
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lawliet
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Reply #18 on: June 26, 2008, 08:19:51 pm »

i just want to ask if a pendulum is made to swing in water,how is the graph look like with period (Ts) against length?
and what is the difference between the time taken for this pendulum (which swings in water) to come to a complete stop and the time taken by a pendulum swinging in air?
if a simple pendulum with a period of 1 second is set in motion on the moon,what is the new period of this pendulum? it will swings forever right?

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Fu-Kwun Hwang
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Reply #19 on: June 26, 2008, 09:00:30 pm »

Please check out Pendulum with damping

The applet assume the damping force is proportional to velocity of the pendulum, which is a good approximation for object moving in water. The applet also assume the mass is always under the water. You can adjust different value for b and find the best one to fit with experimental data. (Because the real damping force also depend on the geometry/area of the pendulum).
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tanhl
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Reply #20 on: July 04, 2008, 08:13:19 pm »

Thank you very much Mr Hwang. Whilst looking for some materials on the simple pendulum, I was really surprised at your amazing website -simulations for experiments in physics. It's an eye-opener for me. I have just downloaded the applet and hope it works! : )

thanks once again for your wonderful work and contribution to the body of knowledge.

tanhl
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Reply #21 on: July 14, 2008, 07:17:27 pm » posted from:Istanbul,Istanbul,Turkey

Hi. İ am new in forum. İ have found very necessery documents in this forum. I need  animations like this to explain Physics to my student.
I have translated Pendulum animation in Turkish for forum use.
Sorry to my english Smiley. not very well..
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Fu-Kwun Hwang
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Reply #22 on: July 14, 2008, 10:49:33 pm »

That is fine. Thank you for your help to translate the message into Turkish. 
You might want to check out some other Turkish version web pages already translated by other.
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Reply #23 on: August 06, 2008, 02:11:19 am »

thanks very interesting this program..-*-
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Reply #24 on: January 06, 2009, 06:28:38 pm »

Sir do u have an applet simulation of a collision of two objects?
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Reply #25 on: May 13, 2009, 08:13:29 pm » posted from:Edith,New South Wales,Australia

Hi there Mr. Hwang,

Excellent program on pendulums. You have made physics interesting all over again.

Anyway, I am doing a project for my 3rd year using SUNSpots, which will naturally be programmed in Java. Would it be alright if I requested for the source code of the program? The pendulum is one which will be very relevant to the program. Thank you.
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Fu-Kwun Hwang
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Reply #26 on: May 14, 2009, 12:06:48 am » posted from:Taipei,T\'ai-pei,Taiwan

You should be able to download the source code now (as attached file)!
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dannydesiliva
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Reply #27 on: September 22, 2009, 01:09:35 pm » posted from:Amritsar,Punjab,India

I have never used a pendulum but would like to start.
I have serached the forums and seen the postings about pendulums but still would like to know more about them. Is there a site that has kind of a pendulum 101 page or two?

how do you know what you want to use for a pendulum or what crystal, etc to use?
so many questions and not much info that I can find.
any help out there?
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yimseo
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Reply #28 on: May 08, 2010, 09:21:13 pm » posted from:Singapore,,Singapore

Thankyou for the information. Very Good Example!
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afrah
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Reply #29 on: June 05, 2010, 08:01:11 pm » posted from:,,Jordan

hello mr. Hwang;
i need the source code for pendulum as i have a small project in java applet and i believe this might help..
please respond as soon as possible.
thanks..
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