NTNUJAVA Virtual Physics Laboratory (Java Simulations in Physics)
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NTNUJAVA Virtual Physics Laboratory (Java Simulations in Physics) > JDK1.0.2 simulations (1996-2001) > Wave > Oscillation and Wave
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Author Topic: Oscillation and Wave  (Read 81085 times)
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Fu-Kwun Hwang
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« on: January 29, 2004, 08:30:24 PM »
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  1. If a spring with a mass m attached to it is slightly stretched or compresses with displacement x. The restoring force is given by Hooke's Law

    2. Fr(x)= - k x ,where k is a constant

    The solution to this equation is a simple harmonic oscillation.

    (negligible mass of the spring).

  2. Consider a spring hanging freely, stretches a length dx when it made to support a load of mass m.

    3. The force becomes F(x) = m g - k x

    The equilibrium position is x = m g / k

  3. Add Damping force:

    4. Suppose there is a viscous damping force Fb= - b v,

    where b is a constant and v is the velocity of the load.

  4. add external force that varies harmonically

    5. Fext = fo sin( cwt )

    1. w2 = wo2 - (b/2m)2
      where wo2 = k/m, wo is the nature frequency of the system

    2. if c=0. then fo = 0.

  5. The net force acts on the mass is F = m g - k x - b v + fo sin( cwt )


How to play?
  1. You can enter values of m, k, b, f( m can also be changed with mouse click on +/- button)



    2. b=0., f=0.simple harmonic motion(SHM)
    b!=0. (try 0.1)damped oscillation
    f!=0. (try 5.0)forced oscillation


  2. You can drag the left mouse button to change the initial position of the mass.

  3. Animation starts when the mouse button is released.

  4. If you drag with right mouse button ( or press ---> Button),

    5. the spring will also move with constant speed in the horizontal direction.

  5. Green arrow : the displacement x measured from the unstretched point.

  6. blue arrow : the displacement x measured from the equilibrium point (F=0).

  7. red arrow : the velocity v of the mass.

  8. Each time you click the mouse button, the coordinate of the mouse is shown in the text Field. (MKS unit, x/v verses t )

  9. External driving force:

    1. c=0. means there is no external force, i.e. fo =0.

    2. otherwise Fext = fo * sin ( c*w* t), where w2 = k/m - (b/2m)2


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There are 2 translations,
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hawk8225
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« Reply #1 on: December 03, 2006, 02:04:55 AM »

finding the amplitude of a wave
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lale
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« Reply #2 on: July 30, 2007, 04:03:48 PM »
please help me Smiley
I can not see the pictures
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Fu-Kwun Hwang
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« Reply #3 on: July 30, 2007, 09:45:36 PM »
If java program did not show up, please download and install latest Java RUN TIME
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sombra55
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« Reply #4 on: November 24, 2007, 12:17:45 AM »
I need to find 5 different examples of SHM and the governing equations besides springs and pendulums. I must be looking in all the wrong places. I have found articles about rocking chairs, swings, and sound waves, ocean waves etc but don't find governing equations and I am not even sure if they are still simple, help please? Huh
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Fu-Kwun Hwang
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« Reply #5 on: November 24, 2007, 07:31:28 AM »
The governing equations for the springs and pendulums can be found at standard textbook or on the web (Have you try to search at wikipedia).
you will find SHM motion, if there is a small enough deviation from stable static equilibrium.
For example: touch the water surface lightly, knock the drum surface...

I guess it is your homework, so you should try to find out the answer by yourself. What you need is knowing what is SHM and looking at everything around you more carefully. And you will find many examples.
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sombra55
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« Reply #6 on: November 25, 2007, 08:06:30 AM »
My issue is what constitutes "different" since shm is all the same? Aren't they all isomorphic to each other? Then they are not different. Also everywhere I read someone is talking about shm and then they deviate and then I am not sure where they began to deviate. For example I know that shm is periodic and that the frequency is constant. The velocity of the oscillator is maximum as it passes thorgh equilibrium and zero as it passes through the extreme positions in it's oscillation. I know there is always a restoring force which always acts toward the equilibrium position. The acceleration is directly proportional to the displacement from the equilibrium position. So you see I have done my homework. I know shm is in springs, pendulums, waves, molecules, Lc circuits. I just wanted to know more than that and how to discern when a writer has deivated from shm, that's all. And oh yeah, I am a graduate student and this is paper I am researching so it's not homework. PS Your spell check is not working, blank screen that says it is done.
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Fu-Kwun Hwang
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« Reply #7 on: November 25, 2007, 10:19:46 PM »
Sorry! There is no way I can know your background and what is the purpose for your post. There are students just post their homework and want someone to answer it for them.

Since you are a graduate student, I am going to assume your are aware of Tayler's expansion.
We can define a potential for an equilibrium system (SHM is a small deviation from an an equilibrium).
U(x)=U(x0)+ dU/dx|x=x0 (x-x0) + (1/2!) d2U/dx2|x=x0 (x-x0)2+(1/3!)d3U/dx3|x=x0 (x-x0)3+ ...
F=-dU/dx ,so

Fx=- dU/dx|x=x0 - d2U/dx2|x=x0*(x-x0) -(1/2!)d3U/dx3|x=x0 (x-x0)2-...
  =- d2U/dx2|x=x0*(x-x0) -(1/2!)d3U/dx3|x=x0 (x-x0)2-...
(because dU/dx|x=x0=0 at equilibrium point x0)

If the higher order term is smaller compared to the first term,
the above equation reduced to Fx=- d2U/dx2|x=x0*(x-x0) = -k *(x-x0)
That is the reason why a small deviation from the equilibrium will show SHM motion if the higher order term is smaller(can be neglect).

For a small wind, the leave on the tree will show SHM motion.
For a stronger wind, branch of the tree will show SHM motion.
For a hugh wind, the whole tree might show SHM motion.

Since you are a graduate student, I will leave the rest to you to think about it. And you will learn something from it. Wink

Thank you for tell me there is something with the spell check function.
« Last Edit: November 25, 2007, 10:31:34 PM by Fu-Kwun Hwang » Logged
sombra55
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« Reply #8 on: November 26, 2007, 12:07:04 PM »
Thanks for the reply. I follow your argument and I understand what you are saying about the Taylor series expansion and that the 3rd derivative is negligible. It also makes sense that a small wind might make a leaf have shm and a little larger might make a branch have shm and a very large wind might make the tree have shm. It's kind of like the angle on a pendulum being "small" having shm and when large it doesn't. Or for the torsional pendulum when the wire is small compared to the relative largeness of the bar. By the way, I am also a math professor at a local college...

spell check still doesn't work, sorry for any typos overlooked...
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Fu-Kwun Hwang
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« Reply #9 on: November 27, 2007, 10:45:06 AM »
Finally, I try to modify the server and the spell checker should work now.
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