3 ms·

Not sure if this is what you mean, but pendulum clocks work because the pendulum "... swings back and forth in a precise time interval dependent on its length,

Not sure if this is what you mean, but pendulum clocks work because the pendulum "... swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates."[0] [0] https://en.wikipedia.org/wiki/Pendulum_clock https://en.wikipedia.org/wiki/Pendulum_clock

jessaustin 11y ago
The fact that a particular mechanism resists the effects of friction doesn't mean it's unaffected by them.
- grahamburger 11y ago
  I don't think that's quite right - friction obviously causes the pendulum swing to slow down, but even as it slows the frequency of the swing remains constant (because the amplitude changes to compensate for the slowed swing) So until the swing actually stops due to friction, the pendulum will continue to keep time. There are of course exceptions, for example if the friction is actually changing (due to air pressure / humidity changes) the clock will go out of sync. This is observable in real life pendulum clocks and I didn't think it was an area of debate - am I missing something here?
  - krastanov 11y ago
    Actually friction changes the frequency, see [1]. Moreover there is this general idea in spectroscopy (whether of atoms or of pendulum clocks) that to precisely measure a frequency you need the smallest dissipation possible (check wikipedia about linewidth-lifetime relations, Q-factors, etc). Basically the precision with which you can measure a frequency is 1/lifetime_of_the_phenomenon. Higher dissipation means lower precision. See [1] https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_har... edit: If this change of frequency is calibrated it is not an issue, but this calibration is not trivial and friction is something a lot less stable than the other physical properties that govern the clock.
- wlesieutre 11y ago
  But (approximating at small angles), the pendulum's period is constant. Friction will have the effect of reducing the distance that it swings, but the amount of time it takes to swing it doesn't change. That's a simplified model of a pendulum and isn't completely accurate, but even if your pendulum has a 30° swing its true period is only 1.7% off of the approximation. And pendulum clocks don't just let the pendulum lose energy to friction until they swing down and stop. Take a look at this deadbeat escapement: https://en.wikipedia.org/wiki/Anchor_escapement#/media/File:Scappamento.gif https://en.wikipedia.org/wiki/Anchor_escapement#/media/File:... (one of several pendulum mechanisms) There are three main actions going on here. 1) A weight is hung so that its downward force is trying to drive the escape wheel's rotation. 2) The side face of the anchor (swinging part w/ pendulum attached) moves in front of the escape wheel tooth and stops it. This locks the motion of the clock mechanism to one tooth per swing (and is the reason the weight doesn't just drop immediately). 3) As the anchor swings off the dead face, the tooth applies a slight push to the sloped impulse face at the end of the anchor. That repeated nudge transfers potential energy from the weight to the pendulum swing, and keeps its swing distance consistent against friction losses. Mechanical clocks are actually pretty clever.
  - krastanov 11y ago
    See my response to grahamburger. Friction does not only cause decay of the amplitude, it also changes the frequency. edit: But you are right, the mechanical clocks are still pretty amazing and quite precise given the limitations of the technology.

jessaustin 11y ago

The fact that a particular mechanism resists the effects of friction doesn't mean it's unaffected by them.

grahamburger 11y ago
I don't think that's quite right - friction obviously causes the pendulum swing to slow down, but even as it slows the frequency of the swing remains constant (because the amplitude changes to compensate for the slowed swing) So until the swing actually stops due to friction, the pendulum will continue to keep time. There are of course exceptions, for example if the friction is actually changing (due to air pressure / humidity changes) the clock will go out of sync. This is observable in real life pendulum clocks and I didn't think it was an area of debate - am I missing something here?
- krastanov 11y ago
  Actually friction changes the frequency, see [1]. Moreover there is this general idea in spectroscopy (whether of atoms or of pendulum clocks) that to precisely measure a frequency you need the smallest dissipation possible (check wikipedia about linewidth-lifetime relations, Q-factors, etc). Basically the precision with which you can measure a frequency is 1/lifetime_of_the_phenomenon. Higher dissipation means lower precision. See [1] https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_har... edit: If this change of frequency is calibrated it is not an issue, but this calibration is not trivial and friction is something a lot less stable than the other physical properties that govern the clock.
wlesieutre 11y ago
But (approximating at small angles), the pendulum's period is constant. Friction will have the effect of reducing the distance that it swings, but the amount of time it takes to swing it doesn't change. That's a simplified model of a pendulum and isn't completely accurate, but even if your pendulum has a 30° swing its true period is only 1.7% off of the approximation. And pendulum clocks don't just let the pendulum lose energy to friction until they swing down and stop. Take a look at this deadbeat escapement: https://en.wikipedia.org/wiki/Anchor_escapement#/media/File:Scappamento.gif https://en.wikipedia.org/wiki/Anchor_escapement#/media/File:... (one of several pendulum mechanisms) There are three main actions going on here. 1) A weight is hung so that its downward force is trying to drive the escape wheel's rotation. 2) The side face of the anchor (swinging part w/ pendulum attached) moves in front of the escape wheel tooth and stops it. This locks the motion of the clock mechanism to one tooth per swing (and is the reason the weight doesn't just drop immediately). 3) As the anchor swings off the dead face, the tooth applies a slight push to the sloped impulse face at the end of the anchor. That repeated nudge transfers potential energy from the weight to the pendulum swing, and keeps its swing distance consistent against friction losses. Mechanical clocks are actually pretty clever.
- krastanov 11y ago
  See my response to grahamburger. Friction does not only cause decay of the amplitude, it also changes the frequency. edit: But you are right, the mechanical clocks are still pretty amazing and quite precise given the limitations of the technology.