What is the significance of elongation in pendulum systems?

In summary, the concept of elongation of a pendulum refers to the stretching of a string or rod that is attached to the pendulum. This phenomenon is often compared to a spring, but it does not affect the equations for a simple pendulum as they assume a massless and rigid string. However, in more complex systems, the elongation of the pendulum can have a measurable effect on the dynamics.
  • #1
wotanub
230
8
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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  • #2


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.
 
  • #3


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.
 

1. What is elongation in a pendulum?

Elongation in a pendulum refers to the change in the length of the pendulum's string or rod from its resting position to its maximum displacement. It is a measure of how far the pendulum swings from side to side.

2. How does the length of the pendulum affect its elongation?

The longer the pendulum's length, the greater its elongation will be. This is because a longer pendulum takes longer to swing back and forth, resulting in a greater distance traveled from its resting position.

3. What factors can affect the elongation of a pendulum?

The elongation of a pendulum can be affected by several factors, including the length of the pendulum, the mass of the bob (weight at the end of the pendulum), the amplitude of the swing, and the force of gravity.

4. How can elongation be calculated in a pendulum?

Elongation in a pendulum can be calculated using the formula E = L(1-cosθ), where E is the elongation, L is the length of the pendulum, and θ is the angle of displacement from the resting position.

5. What is the relationship between elongation and the period of a pendulum?

The period of a pendulum (the time it takes to complete one full swing) is directly proportional to the square root of its length. This means that as the elongation of a pendulum increases, the period also increases.

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