Dynamics of a string coupled pendulum

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Homework Help Overview

The discussion revolves around understanding the dynamics of a string coupled pendulum, particularly focusing on the forces and motions involved. Participants are exploring the implications of simple harmonic motion (SHM) and the complexities introduced by the coupling of multiple pendulums.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the completeness of the problem statement and whether arbitrary oscillation directions and phases need to be considered. There is also a focus on identifying the forces at play, particularly the tensions in the strings and how they interact.

Discussion Status

Some participants are providing qualitative analysis and discussing the complexities of the system, including the number of interacting variables and degrees of freedom. There is an acknowledgment of the challenge posed by the problem, with suggestions for further exploration of the dynamics involved.

Contextual Notes

Participants note that the problem is self-imposed and that the dynamics are not immediately obvious, indicating a potential lack of clarity in the initial setup and assumptions regarding the pendulums' motions.

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Homework Statement



My problem/task is to explain in elementary terms the dynamics of a string coupled pendulum, the same as in this diagram:
VPBT5.jpg


Is it simple to make a free body diagram for the pendulums? Is it possible to understand the motion as being caused by SHM oscillation of the top horizontal spring from which the weighted pendulum are suspended?

Thanks in advance for any help with this problem.
 

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Is this the full statement of the problem? E.g. do we have to consider arbitrary directions of oscillation of the pendula? In arbitrary phases?
 
haruspex said:
Is this the full statement of the problem? E.g. do we have to consider arbitrary directions of oscillation of the pendula? In arbitrary phases?

Assume that initially one of the pendula is displaced at an angle perpendicular to the plane defined by the fixed posts indicated in the diagram, and that the other pendula is initially at equilibrium.

It is a self-imposed problem that I have set myself, to understand the dynamics of this system. Unlike a spring coupled pendulum, the forces involved are not so obvious and I am not sure where to start.
 
Last edited:
This problem can be solved by the technique of Lagrangian dynamics. The solution has a closed form for small angular displacements. It would be fun and easy to set up an experiment to observe the oscillatory transfer of angular momentum from one pendulum to the other.
 
Hi, thanks for the reply. I am looking more for some qualitative analysis. Exactly forces are involved? The tension in the long suspending string, as in the situation for SHM. In addition the tension from the horizontal string must come into account, I guess? Just a bit lost as to how to put all of this together.
 
physics_cosmos said:
Hi, thanks for the reply. I am looking more for some qualitative analysis. Exactly forces are involved? The tension in the long suspending string, as in the situation for SHM. In addition the tension from the horizontal string must come into account, I guess? Just a bit lost as to how to put all of this together.
You have chosen a very complicated problem.
There are five different tensions.
The two junctions between the strings lie on spheres centred at the tops of the posts, but the distance between them adds a constraint, making three degrees of freedom.
At any instant, the three strings at a junction lie in a plane (why?).
The positions of the bobs relative to the junctions have one more degree of freedom each, and their velocities add two more each.
That's nine interacting variables.
 

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