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Considering a pendulum clock does the period of oscillation of the pendulum increase when the clock itself is set in motion due to increase of mass?

jamesfairclear
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    According to whom in what frame? – Jon Custer Jan 10 '22 at 14:52
  • @JonCuster as compared with an identical relatively stationary pendulum clock at the original location. – jamesfairclear Jan 10 '22 at 15:15
  • The period of a pendulum clock depends on gravity. Such a clock moving past at a speed that would produce a noticeable increase in mass would also be subject to a rapid change in gravity. – R.W. Bird Jan 10 '22 at 15:23
  • @R.W. Bird: although quite artificial (because nobody will be able to move a pendulum clock close to the speed of light in the near future), a pendulum clock is not in desperate need of gravity. A constant acceleration is sufficient for the pendulum to work. Moreover, a special relativistic question is always valid locally even in the presence of a gravitational field (just like Einstein used the elevator example to illustrate the equivalence principle locally). Simply watch the clock on the fly-by. Of course, you are right in that this experiment is not very sustainable. – oliver Jan 10 '22 at 15:39
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    Relativistic mass is generally not a helpful concept, see https://physics.stackexchange.com/q/133376/123208 But apart from that, there's no mass term in the equation for the period of a pendulum. – PM 2Ring Jan 10 '22 at 16:21
  • Say if we had a pendulum clock which is synchronised to an atomic clock sitting next to it in an idealised train car at rest on a straight track in a uniform gravitational field. Now set the train moving at a high uniform speed. Do you expect the clocks to go out of synch? – PM 2Ring Jan 10 '22 at 16:26
  • Thank you all for your comments. – jamesfairclear Jan 10 '22 at 20:12
  • @R.W.Bird "Such a clock moving past at a speed that would produce a noticeable increase in mass would also be subject to a rapid change in gravity". Would you expect that relativistic gravity to affect the period of the pendulum? – jamesfairclear Jan 11 '22 at 17:19
  • If the pendulum was on the exterior of a ship in deep space, moving at a very high speed, and with an acceleration of one “g”, I would expect a “stationary” observer would measure a longer period of swing than a person on the ship. As PM 2Ring points out, this should be independent of the mass. An atomic clock on the ship should also appear to run slower, so there would not be a loss of synchronization. – R.W. Bird Jan 12 '22 at 15:27
  • @R.W.Bird so are saying that relativistic gravity is a physical effect due to the motion of the clock and in the vicinity of the clock and separate from the effect of time dilation but not affecting the period of the pendulum in its stationary frame of reference? – jamesfairclear Jan 14 '22 at 08:28

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No. The period of a pendulum clock depends only on the effective length of the pendulum and the acceleration due to gravity- the mass of the pendulum does not affect it.

Marco Ocram
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Here your interpretation goes a bit wrong.

Let's take a look at the equation for the time period of the pendulum that is:

$T=2π \sqrt{\frac{l}{g}}$

Here in this equation we can clearly see that the time period of the pendulum does not depend upon the mass of the bob attached to the pendulum.

So it would be inappropriate to talk about mass here. Which leads to a complete invalid concept.

Tejas Dahake
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It depends on the type of motion... for example, if it were put in a centrifuge (or subjected to some other kind of constant acceleration) then the period of oscillation would certainly change - but this would be due to the increase of weight not mass.

Martin CR
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  • could we then consider the clocks in the HK experiment (assuming pendulum clocks) as in effect being in a centrifuge and the consequent increase in weight resulting in an increased oscillation period in the pendulums? – jamesfairclear Jan 11 '22 at 20:22
  • If you're talking about the Hafele–Keating experiment, then no. The effect would have been similar if they had been travelling in a straight line. – Martin CR Jan 11 '22 at 20:40
  • If you were thinking about the gravitational time-dilation effect in the experiment, it works the other way around: as the gravitational field increases a pendulum clock swings more quickly, whereas the relativistic effect of gravitational time dilation makes a clock appear to run more slowly (from the perspective of an external observer) – Martin CR Jan 11 '22 at 20:48
  • "If you were thinking about the gravitational time-dilation effect in the experiment, it works the other way around". I wasn't thinking about that, but it's an interesting point as a Pendulum clock will automatically counter time dilation. "whereas the relativistic effect of gravitational time dilation makes a clock appear to run more slowly". A clock really does run more slowly in the presence of a gravitational field. A GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day and corrections need to be made. – jamesfairclear Jan 16 '22 at 20:31
  • "If you're talking about the Hafele–Keating experiment, then no. The effect would have been similar if they had been travelling in a straight line.". Why would a clock circling the Earth be different from a clock inside a centrifuge? – jamesfairclear Jan 16 '22 at 20:40