Why doesn't mass of a pendulum effect its time period

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Discussion Overview

The discussion centers around the relationship between the mass of a pendulum and its time period, exploring the principles of potential energy (PE), kinetic energy (KE), and the effects of mass on oscillation. Participants examine theoretical implications and historical context, while questioning common assumptions in physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant argues that increasing mass leads to increased potential energy (PE), which should result in greater total mechanical energy (TME) and thus greater kinetic energy (KE) at the equilibrium position, potentially shortening the time period of oscillation.
  • Another participant challenges the assumption that increased KE directly correlates with increased velocity, suggesting that KE depends on additional factors beyond just velocity.
  • A different viewpoint emphasizes that all masses fall at the same rate in a gravitational field, implying that the time period of a pendulum is independent of mass.
  • Historical context is provided by referencing Galileo's experiments, which suggested that mass does not affect the rate of fall, reinforcing the idea that the time period of a pendulum is not influenced by its mass.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mass and time period, with no consensus reached. Some argue for a direct relationship based on energy considerations, while others assert that mass does not affect the time period due to gravitational principles.

Contextual Notes

Participants discuss the implications of potential and kinetic energy without resolving the complexities of their interdependence. The discussion also reflects on historical interpretations of mass and gravity, which may influence current understanding.

Revin
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I'll jump straight to my query.

If PE = mgh, and if the "m" is increased, the PE shall also increase.
Neglecting friction, Total mechanical energy(TME) = PE + KE.
Since PE increases, the total mechanical energy of the system shall also increase.
At its equilibrium position, where PE = 0, it should have a greater amount of KE since
KE = TME-PE.

Having more kinetic energy, it should hence have more velocity as well.
Hence, having more velocity, its time period should be shortened since it takes lesser time for it to complete one oscillation having the same distance ( Note that the value of h is not changed here).

After all this, why is it practically proven that mass doesn't effect the time period?
 
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Revin said:
If PE = mgh, and if the "m" is increased, the PE shall also increase.
Neglecting friction, Total mechanical energy(TME) = PE + KE.
Since PE increases, the total mechanical energy of the system shall also increase.
At its equilibrium position, where PE = 0, it should have a greater amount of KE since
KE = TME-PE.
OK so far.
Revin said:
Having more kinetic energy, it should hence have more velocity as well.
No. Kinetic energy doesn't just depend on velocity, it depends on something else as well...
 
All masses fall at the same rate.In effect your pendulum is a falling mass with just the right amount of added energy from the mechanism to overcome friction if it's in a clock so it does not stop.
If it's just a pendulum then it's a falling mass on a rope when it swings.
And all masses swing or fall at the same rate within a gravity field.
 
Dear old Galileo sorted this out a long time ago. The story is that he won a bet about dropping masses off the Tower of Pisa. His contemporaries believed that a heavy object would reach the bottom before a light object - he knew better. That's just a story but is shows that reality is often counter-intuitive.
 

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