Harmonic oscillator and simple pendulum time period

Click For Summary
SUMMARY

The discussion centers on the differences between the time periods of harmonic oscillators (HOs) and simple pendulums. It establishes that the time period T of a harmonic oscillator is given by the formula T = 2π√(m/k), where m is mass and k is the spring constant, remaining independent of amplitude. In contrast, the simple pendulum's time period is T = 2π√(ℓ/g), where ℓ is the length and g is the acceleration due to gravity, indicating that T varies with length ℓ. The small angle approximation allows the pendulum's period to be independent of amplitude, but deviations from this approximation introduce amplitude dependence.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with the small angle approximation in physics
  • Knowledge of basic mechanics, including Newton's laws
  • Concept of restoring forces in oscillatory systems
NEXT STEPS
  • Study the derivation of the simple pendulum time period formula T = 2π√(ℓ/g)
  • Explore the implications of the small angle approximation in oscillatory motion
  • Investigate the differences between linear and angular displacement in oscillatory systems
  • Learn about cycloidal motion and its application in pendulum design
USEFUL FOR

Physics students, educators, and anyone interested in the mechanics of oscillatory systems, particularly those studying pendulum behavior and harmonic motion.

  • #31
Physics news on Phys.org
  • #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.
 
  • Like
Likes   Reactions: vanhees71 and PeroK
  • #33
Lord Grimthorpe? You couldn't make it up!
 
  • Haha
  • Like
Likes   Reactions: vanhees71, bob012345 and anorlunda
  • #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?
1660425619158.png
 
  • #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.
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
7K
  • · Replies 1 ·
Replies
1
Views
1K