I Damping in a coupled pendulum system

AI Thread Summary
The discussion focuses on the effects of increased damping on the frequencies of coupled pendula, drawing an analogy with LC resonators. It suggests that adding a damper in parallel with the spring could influence the system's behavior, particularly affecting the "opposite" mode. Participants are encouraged to explore the implications of introducing arbitrary drag on each pendulum. Understanding these dynamics is presented as fundamental to grasping broader concepts in physics. The insights gained from this analysis are considered applicable across various physics scenarios.
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I was going through my old lab experiments ans stumbled upon a coupled pendulum experiment I did few years ago. Now That I have learnt about damping, I was wondering how a damping which would be present in the individual pendulums affect their coupling?
The beat frequency was equal to the difference in frequencies of the two normal modes. What would be the beat frequency in the case of damping present?
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From analogy with LC resonators, I think the increased damping will move the two frequencies further apart.
 
I think you should first think about putting a damper on (in parallel with) the spring. You know intuitively only the "opposite" mode would be affected. Work that through in detail.
Then put an arbitrary drag on each pendulum and work it out.
If you really understand this system you are looking at half of known physics IMHO. We use it over and over.
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

This argument is another version of my previous post. Imagine that we have two long vertical wires connected either side of a charged sphere. We connect the two wires to the charged sphere simultaneously so that it is discharged by equal and opposite currents. Using the Lorenz gauge ##\nabla\cdot\mathbf{A}+(1/c^2)\partial \phi/\partial t=0##, Maxwell's equations have the following retarded wave solutions in the scalar and vector potentials. Starting from Gauss's law $$\nabla \cdot...
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