### Author Topic: Simple Harmonic Motion and Uniform Circular Motion  (Read 551644 times)

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Simple Harmonic Motion and Uniform Circular Motion
« on: January 29, 2004, 04:10:12 pm »
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The force for a spring with displacement \$vec{x}\$, spring constant k is \$vec{F}(x)=-kvec{x}\$ (Hook's Law).
From Newton's law \$vec{F}=m vec{a}=m frac{d^2 x}{dt^2}\$
So \$m frac{d^2x}{dt^2}=-k x\$.
The solution of the above equation is \$x=A sinomega t\$.
Since \$ frac{dx}{dt}= A omega cosomega t\$, \$frac{d^2x}{dt^2}= -A omega^2 sinomega t=-omega^2 x\$
So \$omega=sqrt{frac{k}{m}}\$.
If the spring is moved away equilibrium position, it will move with displacement similar to \$x=A sinomega t\$, which is called simple Harmonic motion (SHM).

The following applet shows relation betweeb simple harmonic motion and spring motion.

\$frac{x^2}{a^2}+frac{y^2}{b^2}=1\$, \$x(t)=a*sin(omega t), y(t)=b*cos(omega t)\$

The uniform circular motion is intimately related to a simple harmonic motion.
If we were to look at a side view of the uniform circular motion
on a thumbtack stuck on a rotating table,
we would see the thumbtack oscillate in simple harmonic motion.

Press Start to begin the animation.
The black dot will move in uniform circular motion.

Watch and find out the relation between uniform circular motion and simple harmonic motion.

Press left mouse button to suspend the animation, press it again to resume.

Did you find out the frequency of the uniform circular motion?

The red arrow represents the velocity of the black dot.

The yellow arrow and the blue arrow are components of the above velocity vector.

Did you know when the thumbtack has maximum velocity ?

If you click the left mouse button within the dark-gray area , and drag the mouse button left/right,

you can rotate the circle about the vertical axis. (sample picture)

You can rotate the circle 90 degree => side view of the motion.

( This feature was added as a request from B. Surendranath Reddy.)

The above clip is actually adopted from "The mechanical universe" series.

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

• Guest
##### topic148
« Reply #1 on: January 30, 2004, 12:30:52 pm »
Date: 8 Feb 99 16:40:40 PST
From: shefali oza <shefalib@netscape.net>
To: hwang@phy03.phy.ntnu.edu.tw
WOW! my physics teacher (Mrs. Woolard) suggested your website as an extremely
useful tool to help us learn about oscillations and SHM, as well as other
physics concepts. your site really is truly wonderful and it is obvious that
you have put plenty of time into making it. it has been very helpful in
clarifying some places where i was having difficulties. i am so glad my
like to congratulate you on such a wonderful job.
shefali oza (north carolina)

• Guest
##### topic148
« Reply #2 on: January 30, 2004, 12:31:14 pm »
Date: Mon, 8 Feb 1999 20:55:47 EST
From: Bananas337@aol.com
To: hwang@phy03.phy.ntnu.edu.tw
your webpage is awesome! my physics teacher, Ms. Woolard,
(lizwoolard@hotmail.com) assigned us your webpage as our homework tonite. you
have done a great job! thanks!

stephanie yeh
bananas337@aol.com

• Guest
##### topic148
« Reply #3 on: January 30, 2004, 12:46:35 pm »
Subject: Applets
Date: Thu, 22 Apr 1999 18:20:15 +0100
From: "Anthony Vinters" <Tony@g0wfg.demon.co.uk>
To: <hwang@phy03.phy.ntnu.edu.tw>
Dear Fu Kwun Hwang
Thank you for the Applets, they are excellent! I have used them for teaching
my students about Simple Hamonic Motion and the Principle of Superposition.
Have you done one which shows the motions of particles within a Transverse
Wave and a Longitudinal wave? It would be interesting to look at the
particle motion and compare them within these two wave systems. If it were
possible to show the phase relationship between any of the particles even
better! Showing that any particles that are 2Pi radians out of phase with
each other are 1 wavelength apart is something that students can find
difficult to understand without the help of a moving model.
Once again thank you for all your work.
With best wishes:
Mr.A.E.Vinters.
Rishworth School

• Guest
##### topic148
« Reply #4 on: January 30, 2004, 12:47:33 pm »
Subject: Re: Applets
Date: Mon, 26 Apr 1999 23:44:29 +0100
From: "Anthony Vinters" <Tony@g0wfg.demon.co.uk>
To: "Fu-Kwun Hwang" <hwang@phy03.phy.ntnu.edu.tw>
Dear Fu Kwun Hwang,
I have received your applet. This is fine, the diagrams look exactly
right. I cannot run the applet as my email seemed not to contain any
software to animate the diagrams, only the pictures themselves. Can
you put this on your site so I can try it out?
Perhaps you would consider writing an applet to show a how a
Transverse wave is made up of oscillating particles: this would be a
most valuable teaching tool.Also a Longitudinal wave to show how the
wave particles vibrate in the same plane as the plane of propagation?
Both applets would work well alongside your excellent SHM applet.
Once again thank you for answering my request, certainly material
such as this makes Physics much more enjoyable to teach and learn.

With very best wishes,
Anthony Vinters. Head of Science Rishworth School.

#### Duncan McLellan

• Physics teacher
• Newbie
• Posts: 1
• sailing
##### Re: Simple Harmonic Motion and Uniform Circular Motion
« Reply #5 on: February 21, 2005, 10:42:05 pm »
I teach Physics to 16-19 year old students and I have already used your SHM Applets in class using a data projector. They are excellent. Is there anyway in which I can download them and run them off our network?

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### topic148
« Reply #6 on: February 22, 2005, 10:24:37 am »
May be you did not notice that there is a button at the end of the first message labeled
"GET APPLET FILE".

#### Mick

• Newbie
• Posts: 1
##### topic148
« Reply #7 on: October 08, 2005, 10:07:17 am »
Hi this is really cool. i like the red yellow and blue vectors. :shock:

Is it possible i can get the Java source code for this app? I would like to see if i can do something similar but with different shapes. not just circles, but cams and trilobes and ellipses

I be happy to post my changes back to the forum

#### Nat Hager III

• Newbie
• Posts: 1
##### topic148
« Reply #8 on: January 21, 2006, 02:41:48 am »
I downloaded the applet for off-line use, but the fonts are unreadible. Can you tell me what I'm doing wrong?

Nat Hager

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### topic148
« Reply #9 on: January 23, 2006, 09:42:14 am »
Usually the zip file cantains more than one html files.
Index.html is the Chinese version, and other html files are for different language version.
Please check out other html files.

Fu-Kwun :-)

#### Physics88

• Newbie
• Posts: 1
##### topic148
« Reply #10 on: January 24, 2006, 09:23:26 pm »
Thanks to all of the people who designed this web site.My term homework was physics simulations and I found everything I wanted in this site.Thanks again.

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### topic148
« Reply #11 on: January 25, 2006, 02:06:16 pm »
You are welcomed! :-)

#### mma943

• Newbie
• Posts: 4
##### Thanks
« Reply #12 on: December 14, 2006, 09:50:53 pm »
Thanks for this topic

#### scotbilt

• Newbie
• Posts: 1
##### Re: Simple Harmonic Motion and Uniform Circular Motion
« Reply #13 on: November 13, 2007, 01:03:56 pm »
Dear Fu-Kwun Hwang,
I am sorry for trying to download so many applets in such a short time frame.  I am a physics student and quite near finishing a degree to teach high school natural sciences.  These applets will be very useful to me in the classroom later in my career.  Also, in my Physics for Teachers course we have to teach 50 minute classes every week and a half so it is nice to have these for demo purposes.
Thanks very much for all your hard work, time, and consideration,
Scott Biltoft