What equations are used for coupled pendulums?

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  • Thread starter Thread starter Callum Johnston
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Discussion Overview

The discussion revolves around the equations applicable to coupled pendulums, specifically focusing on two separate pendulums on strings rather than those that are conjoined or connected by springs. Participants explore the equations related to energy, velocity, period, and frequency, while also considering how changes in length and distance between the pendulums might affect the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants mention equations such as ∆E = mg∆h, v = √2g∆h', t = 2π√l/g', and f = 1/t as relevant to the analysis of the pendulums.
  • One participant expresses confusion about the system and requests a diagram for clarification, indicating a need for a better understanding of the setup.
  • Another participant inquires about how to explore dependent and independent variables when changing the lengths of the pendulums and the distance between them.
  • There is a suggestion that the dynamics of the system could be similar to those of coupled pendulums with a spring, proposing that the string connecting the pendulums could act similarly to a spring in terms of perturbation effects.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specific equations or the nature of the system, as there are varying interpretations and requests for clarification. Multiple competing views and uncertainties remain regarding the setup and the equations applicable to it.

Contextual Notes

Some limitations include the lack of clarity on the system's configuration, missing assumptions about the nature of the coupling, and unresolved questions about the impact of changing variables.

Callum Johnston
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This is for just two separate pendulums on a string, not conjoined pendulums or ones with a spring between them. All I can think of is ∆E = mg∆h, v = √2g∆h', t = 2π√l/g' and f = 1/t.
 
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Callum Johnston said:
This is for just two separate pendulums on a string, not conjoined pendulums or ones with a spring between them. All I can think of is ∆E = mg∆h, v = √2g∆h', t = 2π√l/g' and f = 1/t.
I do not understand the system. could you explain the situation with a diagram? Also, what is the question?
 
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What equations could you use to explore the dependent and independent variables if I plan to change the length of the pendulums and the distance between them?
 
It's the same as with a spring between them. The spring here is essentially the string connecting them at the top.

I suppose you could consider a delay as the perturbation travels from the swinging part to the spring string.
 

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