# Connected Pendulums: Momentum Transfer Time

• silentbox
In summary, a student is trying to determine the time needed for one full transfer of momentum between two string-bob pendulums of identical length and mass suspended on a loosely hanging rope. The experimental results suggest a linear relationship, but the uncertainties and lack of advanced knowledge in oscillations make it difficult to confirm. Some suggest using Lagrangian mechanics to solve the problem. This phenomena is also known as "beating".
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?

silentbox said:
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...

You mean "loosely hanging rope" like this:

Last edited by a moderator:
Care to share your data with us?

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.

Epic_Sarthak said:
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.

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

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.

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

silentbox said:
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?

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

You must have studied Newtons second law :

F=dp/dt

Now let's 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

silentbox said:
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?

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.

## What is a connected pendulum?

A connected pendulum is a system of two or more pendulums that are linked together with a rigid rod or string. This allows for the transfer of momentum between the pendulums, resulting in synchronized motion.

## How does momentum transfer occur in connected pendulums?

Momentum transfer in connected pendulums occurs when one pendulum is set in motion, causing the other pendulums to also start moving due to the transfer of energy through the connecting rod or string. This results in a synchronized swinging motion of all the pendulums.

## What factors affect the momentum transfer time in connected pendulums?

The length of the connecting rod or string, the mass of the pendulums, and the initial angle at which the pendulums are released all affect the momentum transfer time in connected pendulums. Additionally, the presence of air resistance and friction can also impact the transfer time.

## Can the momentum transfer time be predicted in connected pendulums?

The momentum transfer time in connected pendulums can be predicted using mathematical equations that take into account the factors mentioned above. However, due to the complex nature of the system, the predictions may not always be accurate and experimental data may be needed for more precise results.

## What are the real-world applications of studying connected pendulums and momentum transfer?

Studying connected pendulums and momentum transfer can have various real-world applications, such as understanding and modeling the behavior of synchronized systems in nature, designing and optimizing energy transfer systems in engineering, and even investigating the dynamics of social interactions and communication networks.

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