0
$\begingroup$

We have 6 particles. We couple them 2 by 2 with a spring of strength $K$ (as in the picture below). We then have 3 harmonic oscillators. Then we couple each oscillator by a spring of strength $S\ll K$ (i.e. the strength is much smaller than $K$... We call it a weak coupling). But I think it's not important for my question.

Anyway, the situation is shown on the picture 1 below. My problem is I really can't imagine such a mouvement. For example, in the picture 2 (when spring are attached to a wall), I really can imagine such a mouvement, but when it's not connected to a wall and is free like in picture 1, I can't see how such a mouvement could be. Does someone has a example in the nature ? Or a simulation ? Or can tell me where such a mouvement can happen in the nature ?

enter image description here

Picture 1 enter image description here Picture 2

$\endgroup$
4
$\begingroup$

I was interested in this question, so I built a model using Mathematica 11.3. Here is an example of the movement of 12 particles mass of $m=1$ connected with springs of different strength coefficients $k_1=990,k_2=10$. Particles are initially located on a circle. Then in the process of movement a hexagonal structure is formed. The numbers correspond to particles that were numbered in the initial state. The numbers above the pictures correspond to the time. fig1 After several periods of oscillation, the hexagonal structure is transformed into a less symmetrical one, and the movement becomes similar to chaotic.

fig2 The movement of the system is shown below. fig4

The case of ten particles is also interesting. A pentagram is formed from 10 particles in the process of movement. fig5

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Could you please send me the mathematica codes ? That would help me a lot to play with other coupling. $\endgroup$ – idm Feb 5 '19 at 13:45
  • $\begingroup$ Where to send the code? $\endgroup$ – Alex Trounev Feb 5 '19 at 14:17
0
$\begingroup$

Situations like this were explored on an air bench in physics lab forty odd years ago. Bodies with different masses were coupled with springs of different spring constant and moved by sound at different frequencies to identify the normal modes. I am not aware of simulations though. In some sense the stronger spring could correspond to the force between atoms in a water molecule and the weaker to the intermolecular forces. As for visualization, when there is a wall one of the two ends of the spring is fixed. When both bodies move, the distance between the two bodies changes. If one neglects friction one can calculate the frequencies at which the system resonates.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.