# Connected pendulums

1. Jun 17, 2011

### silentbox

Hello.

I have two string-bob pendulums of identical length and mass suspended on a loosely hanging rope. I set one of the pendulums into oscillations and notice that the two begin to slowly "trade" the momentums, ie after a moment the first one comes to a halt when the second is now oscillating with the original amplitude of the first one. The situation now reverses.

I'm trying to determine how the time needed for one full transfer of momentum between the two pendulums will depend on their length (which is identical for both). The experimental result I obtained suggests the relation is linear, but I'm not so eager to believe it. The uncertainties are too big for me to really be sure about anything. I can't develop a theoretical model because the topic of oscillations we covered in class is not very advanced and I just wouldn't know how to go about that. Could you help me out and suggest a theoretical solution?

2. Jun 17, 2011

### Spinnor

You mean "loosely hanging rope" like this:

Last edited by a moderator: Sep 25, 2014
3. Jun 17, 2011

### Spinnor

Care to share your data with us?

4. Jun 21, 2011

### Epic_Sarthak

Well, when one bob strikes the other, it transfers its full momentum and energy to the other one and vice versa.

After that, you have to share more data of your experiments and observations so that we can help.

5. Jun 21, 2011

### Yuqing

He said it was a slow transfer. This is due to resonance. Nothing is colliding.

6. Jun 22, 2011

### schip666!

Look up "coupled pendulums" and "coupled oscillators". I wish I could point you to a some simple math, but it's actually a complex problem....

I think with (nearly) equal periods you will get a linear, or maybe sine, function of energy translated back and forth. But in the general case this is a classical non-linear chaotic system that demonstrates sensitive-dependence-on-conditions. These systems may be easily modeled -- as one of my friends says, any physics major can derive the equations of motion...even though he never offered to derive them for me -- but the solutions to the equations are often only found by numerical iteration.

7. Jun 24, 2011

### Shoku Z

Check the Push Me-Push You spring problem from Kleppner-Kolenkow(Momentum transfer and SHM).Its similar.

8. Jun 26, 2011

### sankalpmittal

You must have studied newtons second law :

F=dp/dt

Now lets make an equation :

T=2*pi*l1/2/g1/2

But if the movement of pendulum is slow then there is force constant being applies as its the matter of resonance .

F=mv/t-->1
=mv/2*pi*l1/2/g1/2

so F= p/2*pi*l1/2/g1/2

Thus F2 is inversely proportion to L if T is kept constant

Or F2 is inversely proportion to T2 if L is kept constant

9. Jun 26, 2011

### Nirgal

Have you discussed Lagrangian mechanics yet? It is easiest to use Lagrangian mechanics to solve coupled oscillator problems such as this. You have to write down the Lagrangian of the system and then solve Lagrange's equation of motion. If you want to find any dependence on length it will be in there. Taylors Classical Mechanics discusses such a problem.

The phenomena you're describing when the pendula transfer's their momentum such that one becomes still while the other begins moving is called "beating". You might try looking up "Beating" on google....though you might try adding physics or something afterward otherwise you might get some strange results.