Period and frequency of a pendulum doesn't depend on mass?

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Discussion Overview

The discussion centers on the relationship between the mass of a pendulum bob and its period and frequency of oscillation. Participants explore the implications of the formulas for period (T) and frequency (f) of a pendulum, questioning why mass does not appear in these equations and how this aligns with intuitive understandings of motion and acceleration.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the formulas for period and frequency of a pendulum do not include mass, leading to confusion about why a lighter pendulum bob should not swing faster when pushed with the same force.
  • Another participant explains that while a heavier pendulum experiences a greater force, it also requires a greater force for a given acceleration, suggesting that these effects cancel each other out.
  • A participant presents a thought experiment involving two identical pendulums, questioning whether combining their masses would affect their frequency, despite the equations indicating it would not.
  • Some participants argue that while a lighter child on a swing may accelerate faster, the increased distance traveled results in a constant time period, supported by the principle of conservation of energy.
  • There is mention of the effect of the swept angle on time, though it is noted that this effect is minimal until the angle becomes large.
  • One participant asserts that the relationship between distance traveled and speed for an ideal pendulum is independent of mass, suggesting a disconnect between intuitive explanations and real-world behavior.

Areas of Agreement / Disagreement

Participants express differing views on the implications of mass on the pendulum's motion, with some supporting the idea that mass does not affect frequency while others maintain that intuitive understandings suggest otherwise. The discussion remains unresolved regarding the relationship between mass and oscillation characteristics.

Contextual Notes

Participants reference the conservation of energy and the effects of swept angle, but there are unresolved assumptions regarding the ideal conditions of the pendulum and the applicability of the discussed concepts in real-world scenarios.

gkangelexa
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Period and frequency of a pendulum doesn't depend on mass??

for a pendulum:

T = 2\pi\sqrt{}length/g

and f = 1/2\pi \sqrt{}g/length


The mass m of the pendulum bob doesn't appear in the formulas for T and f of a pendulum
where T = period
and f = frequency

How does this make sense? If you use a force to push a light child on a swing and use the same force to push a heavy child on a similar swing, the light child should swing faster, right?

bc F = mass x acceleration ... so the one with the lighter mass should accelerate faster therefore its frequency should be higher...?

but according to those equations, the mass doesn't play a role... why?/ how?
 
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The more a pendulum weighs, the higher the force it feels. But the more a pendulum weighs, the higher the force needed for a given acceleration. These two effects exactly cancel.
 


gkangelexa said:
f = 1/2\pi \sqrt{}g/length
Quick lesson on TeX :rolleyes: : f = \frac{1}{2\pi}\sqrt{\frac{g}{l}}

gkangelexa said:
the light child should swing faster, right?
... so the one with the lighter mass should accelerate faster therefore its frequency should be higher...?
Light child would swing faster and with higher acceleration, but frequency will be the same - higher force/acceleration/velocity results with higher amplitude of oscillations, but the frequency remains the same.

Take Galileo's-like thought experiment: two identical penduli, oscillating side by side with another. Now put a drop of glue between iron balls - now you have one pendulum of twice bigger mass. Should this drop of glue change their frequency?
 


(wow how did you make that in fraction form? haha)

Conceptually, it makes sense to me that their frequency should change too... but according to the equation it doesn't change...
 


Well, your concept is wrong! As xts said, if you apply the same force to a lighter child (or pendulum bob) you will give that child a greater acceleration so it will move faster. But that faster speed will result in the child going further. The speed will be greater but the distance traveled will be greater with the net result being that the time taken to travel is constant. The fact that the greater distance traveled at that greater speed is exactly enough to keep the time constant comes from the "conservation of energy".
 


The swept angle does affect the time, but not by much until the angle gets large. Wiki article with formulas. Although the article mentions θ in units of degrees, in the infinite series formula, θ is in radians.

http://en.wikipedia.org/wiki/Pendulum
 


HallsofIvy said:
The speed will be greater but the distance traveled will be greater with the net result being that the time taken to travel is constant. The fact that the greater distance traveled at that greater speed is exactly enough to keep the time constant comes from the "conservation of energy".



I think i understand your explanation the best. thanks!
 


I'm afraid the distance traveled and the speed at which it travels is (for an ideal pendulum) independent of mass. So while it may be the easiest explanation to understand, it does not match the real world.
 

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