Experiment regarding two pendulums which are linked

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In summary, a experiment was conducted involving two linked pendulums connected by a rubber band. The independent variable was the distance between the rubber band and the platform. The time period of a cycle was timed, but there is confusion about the mathematical relationships involved. The pendulum's energy is thought to be kinetic, but the velocity is unknown. The rubber band may play a role in the energy transfer, possibly through its first harmonic. The wavelength of the rubber band is thought to be double its length, but the frequency cannot be calculated. The rate of energy transfer is also unclear. The person asking for help is confused and seeking assistance.
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WaterMelllon1
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Homework Statement



A experiment has been conducted. Two pendulums (oscillators) are linked through a rubber band (it connects the strings of the oscillators). Force is exerted on one pendulum and the energy transfers from this pendulum to the next one. The time period of a cycle (when the second pendulum stops again) is timed, and the independent variable is the distance between the rubber band and the platform the pendulums are connected to.

2. Homework Equations and my thoughts on this

I have little grasp on the mathematical relationship behind this experiment. I think the pendulum's energy is kinetic, Ek=1/2mv2, but although the mass is known. The velocity is unknown. I have an idea that this may be angular velocity, meaning w=2π/T, so will the kinetic energy then be calculated via the equation Ek=1/2m(2π/T)2?

However, these relationships still do not link the displacement from the platform to the rubber band with the time period of a cycle of oscillation. Does this have to do with the medium of the energy transfer? In this case, the rubber band? I think the rubber band oscillates during the experiment at its 1st harmonic and the energy is transferred through that. The wave length should be double the length of the rubber band. I also thought about using the formula v=λf, since λ can be worked out, but I can't calculate the frequency.

I also believe this has something to do with the rate of the transfer of energy, but I have no idea how I can find that.

What I said maybe all wrong, I really am confused about this experiment.

Thank you very much for the help
(Edit: formating)
 
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3. The Attempt at a SolutionI have little grasp on the mathematical relationship behind this experiment. I think the pendulum's energy is kinetic, Ek=1/2mv2, but although the mass is known. The velocity is unknown. I have an idea that this may be angular velocity, meaning w=2π/T, so will the kinetic energy then be calculated via the equation Ek=1/2m(2π/T)2? However, these relationships still do not link the displacement from the platform to the rubber band with the time period of a cycle of oscillation. Does this have to do with the medium of the energy transfer? In this case, the rubber band? I think the rubber band oscillates during the experiment at its 1st harmonic and the energy is transferred through that. The wave length should be double the length of the rubber band. I also thought about using the formula v=λf, since λ can be worked out, but I can't calculate the frequency.I also believe this has something to do with the rate of the transfer of energy, but I have no idea how I can find that.I am quite baffled by this problem and would be very grateful for any help. Thank you for your time.
 

FAQ: Experiment regarding two pendulums which are linked

How do the two pendulums affect each other when they are linked?

When the two pendulums are linked, they will synchronize their movements and swing in unison. This is due to the phenomenon of sympathetic motion, where the energy of one pendulum is transferred to the other through the string or rod connecting them.

What factors can affect the synchronization of the linked pendulums?

The length and weight of the pendulums, as well as the length and stiffness of the connecting string or rod, can affect the synchronization of the pendulums. Additionally, external factors such as air resistance and friction can also impact the synchronization.

How does the amplitude of one pendulum affect the other when they are linked?

The amplitude, or the maximum distance the pendulum swings from its resting position, of one pendulum will affect the amplitude of the other when they are linked. If one pendulum has a larger amplitude, it will transfer more energy to the other pendulum, causing it to swing with a larger amplitude as well.

Can the linked pendulums ever become unsynchronized?

Yes, the linked pendulums can become unsynchronized if external factors such as air resistance or friction disrupt the energy transfer between them. Additionally, if the pendulums are not identical in length or weight, they may also become unsynchronized over time.

What is the practical application of studying linked pendulums?

Studying linked pendulums can help scientists understand the principles of resonance and sympathetic motion, which have practical applications in fields such as seismology, engineering, and music. Additionally, linked pendulums can also be used as a visual demonstration of the concept of energy transfer and synchronization.

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