B Harmonic oscillator and simple pendulum time period

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The discussion explores the differences between simple pendulums and harmonic oscillators (HOs), specifically regarding their periods of oscillation. It highlights that while a harmonic oscillator's period is independent of amplitude, a simple pendulum's period is affected by its length, as described by the formula T = 2π√(ℓ/g). The conversation emphasizes that the mass of the pendulum does not influence the period when using the small angle approximation, as it cancels out in the equations of motion. Additionally, it points out that deviations from the small angle approximation lead to amplitude affecting the period. The mechanics of grandfather clocks are also mentioned, noting that they incorporate energy restoration mechanisms that differentiate them from ideal simple pendulums.
  • #31
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  • #32
malawi_glenn said:
We need a "pendulum clock" thread and insight article :)
The timing is poor because people lost interest in mechanical clocks in the 1970s because electronics became the future. However, the Internet didn't soar until the 1990s. That leaves little left online about the subject. However, some traditional books still survive. Here's one I just found.

Clockmaking - Past And Present:,' By The Late Lord Grimthorpe
This vintage book contains a complete guide to clocking making. This text is a veritable must-have for anyone with a keen interest in clocks and watches, and includes detailed, interesting information on the history of clock making, descriptions of the inner machinations and composition of clocks, and much more besides. Although old, the information contained herein is timeless, and will be of as much utility to modern readers as it was to those contemporary with its original publication. The chapters of this book include: A history of clocks and watches, Materials, Tools, Wheels and pinions, Escapements, Pendulums, Motive power, Striking mechanisms, Lantern clocks, Long case clocks, Bracket clocks, The age of a movement, Clock hands, British clocks for export, etcetera. We are republishing this antiquarian volume now in a modern, affordable edition complete with a new introduction on the history of clocks and watches.

By the way, I hope that Google's parent survives long enough for the 40 million books scanned by Google Books, to all become public domain so that their contents can become as searchable as post-book information. Otherwise, the knowledge of millennia may become as lost to mankind as the former contents of the Library at Alexandria.
 
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  • #33
Lord Grimthorpe? You couldn't make it up!
 
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  • #34
anorlunda said:
Atmospheric clocks use harvested energy to rewind the spring, not to drive the clock directly.
I wasn't aware these are still made. Thanks.
 
  • #35
Harvesting energy? Is that what is taught in field theory courses?
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  • #37
The force applied to the mass is the same no matter how long it is (at least for small angles), so the tangential velocity is the same too. The angular velocity is not the same because of:

w = v/L

The angular velocity for a longer L is less, and for a shorter L more. You need more time to pass the same angle with longer L because arc length is longer.
 

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