What is the significance of elongation in pendulum systems?

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SUMMARY

The discussion centers on the concept of elongation in pendulum systems, specifically addressing how the string of a pendulum can be viewed similarly to a spring that can stretch but not compress. The participants clarify that traditional equations for simple pendulums, such as ω = √(g/l), assume a massless and rigid string, which is why elongation does not appear in these equations. The conversation also touches on the implications of elongation for the dynamics of coupled pendulums and the normal modes associated with them.

PREREQUISITES
  • Understanding of simple pendulum mechanics
  • Familiarity with spring constants and elasticity
  • Knowledge of normal modes in coupled oscillators
  • Basic grasp of classical mechanics equations
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wotanub
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Elongation of a pendulum?

Not really a specific question just something in general.

When discussing simple pendulums (a ball on the end of a string) or any system involving strings, my textbook always refers to something as the "elongation" of the string?

Before this, I had never heard of this! When you swing a pendulum, is the string longer at some times than others? How does that work? What causes this? What effect does it have on the motion of the pendulum?

I asked a professor today and he said something like a string can be considered as something like a spring that can be stretched, but not compressed, and there can be a spring constant associated with it. If this is so, then why doesn't this "elongation" factor show up in equations like ω = √(g/l) for the simple pendulum, and what does it mean for the normal modes of coupled pendulums? I was trying to ask him all these questions, but his English isn't so good to have a long discussion.
 
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wotanub said:
I asked a professor today and he said something like a string can be considered as something like a spring that can be stretched, but not compressed, and there can be a spring constant associated with it. If this is so, then why doesn't this "elongation" factor show up in equations like ω = √(g/l) for the simple pendulum, and what does it mean for the normal modes of coupled pendulums? I was trying to ask him all these questions, but his English isn't so good to have a long discussion.

This is right. The reason it doesn't show up in these equations is because they're just that: simple pendulum equations. They assume the 'string' or 'rod' or whatever it is on the pendulum is a) massless and b) perfectly rigid. One could do an analysis assuming otherwise, but for a lot of physical systems these assumptions are pretty good.
 


In what case dies the elongation of a pendulum have a measurable effect on the dynamics of a system? You would think such a phenomena would have an effect on the equations of motion.
 

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