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My kitchen clock has a pendulum, which is just for decoration and is not powering the clock. The pendulum's arm has a magnet that is repelled by a second magnet that is fixed to the clocks body. The repelling magnets are at their closest when the pendulum is at its lowest point.

We all (hopefully) agree that a regular pendulum would eventually slow down due to friction. But I honestly cannot recall ever seeing the clock's pendulum at rest.

By my calculations the magnet would slow the pendulum as it falls but accelerate it as it swings up the other side. So how would a magnet actually create any net benefit to the pendulum?

Will the pendulum eventually stop, or if not, how is it not violating the laws of thermodynamics?

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    $\begingroup$ I cleaned out some unnecessary comments, and I've made an edit that I think is necessary to make the question a lot better without really invalidating the answers. $\endgroup$
    – David Z
    Commented Feb 11, 2018 at 1:12
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    $\begingroup$ you killed a brilliant meme $\endgroup$
    – minseong
    Commented Feb 11, 2018 at 23:29

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The pendulum is being driven by the magnet: the fixed magnet in the clock is actually the pole of an electromagnet which the clock is using to drive the pendulum: the clock is putting energy into the pendulum via the electromagnet. Almost certainly the clock 'listens' for the pendulum by watching the induced current in the electromagnet, and then gives it a kick as it has just passed (or alternatively pulls it as it approaches).

People have used techniques like this to actually drive a time-keeping pendulum (I presume this pendulum is not keeping time but just decorative) but I believe they are not as good as you would expect them to be, because the pendulum is effectively not very 'free'. 'Free' is a term of art in pendulum clock design which refers to, essentially, how much the pendulum is perturbed by the mechanism which drives it and/or counts swings, the aim being to make pendulums which are perturbed as little as possible. The ultimate limit of this is clocks where there are two pendulums: one which keeps time and the other which counts seconds to decide when to kick the good pendulum (and the kicking mechanism also synchronises the secondary pendulum), which are called 'free pendulum' clocks.

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    $\begingroup$ One grade-school that I attended had an antique synchronous clock system: The wall clocks in the classrooms were all "repeaters," driven by a master clock in the office. The master clock was a tall case clock (grandfather clock) that used an electric drive just like you described. An electromagnet powered the pendulum, which then drove the time keeping gears via a ratchet mechanism. $\endgroup$
    – Solomon Slow
    Commented Feb 9, 2018 at 14:19
  • $\begingroup$ @jameslarge: I own a 'master' clock for such a system (although mine uses what's called a 'gravity arm' escapement, which is electrically reset but actually driven by gravity. $\endgroup$
    – user107153
    Commented Feb 9, 2018 at 16:24
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    $\begingroup$ About the last paragraph, an example of such a time-keeping device is the Shortt pendulum. $\endgroup$
    – Massimo Ortolano
    Commented Feb 10, 2018 at 20:35
  • $\begingroup$ @MassimoOrtolano: yes. When I become ruler of the world I am going to obtain one of them, because they are just astonishing bits of engineering. $\endgroup$
    – user107153
    Commented Feb 11, 2018 at 18:19
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    $\begingroup$ @tfb That's an interesting condition for obtaining one... $\endgroup$
    – Michael
    Commented Feb 11, 2018 at 19:34
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To answer the question directly - No. Your clock is not violating the Laws of Thermodynamics.

If (as you suspect) the pendulum is purely decorative, then, as tfb states, the fixed magnet is an electromagnet that is being driven by an oscillating current. This provides an oscillating field to kick the pendulum in phase with its swing; same way a dad keeps his kid swinging at the park. Nothing more to it.

On a side note, you mention that the pendulum is not "powering" the clock; it's worth pointing out that pendulums never power clocks. In a classic old Grandfather clock, the power is supplied by descending weights or a coiled-spring which have to be wound up. As it unwinds, it provides a torque to turn the clock mechanism. The purpose of the pendulum is to regulate the rate at which the mechanism turns. It does this by means of an escapement - an ingenious little widget that releases the energy in regular packets. Here is a simple example:

An image of an escapement in action as seem on Wikipedia.

https://commons.wikimedia.org/wiki/File:Anchor_escapement_animation_217x328px.gif

The escapement also gives the pendulum a little kick with every tick (or tock) thus ensuring that it keeps swinging.

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    $\begingroup$ "it's worth pointing out that pendulums never power clocks" Well, theoretically, a clock could be. "In a classic old Grandfather clock, the power is supplied by a coiled-spring which is frequently wound up." No, generally the power comes from weights that slowly descend. In fact, the long case of a grandfather clock was originally designed to house these weights. $\endgroup$
    – Acccumulation
    Commented Feb 9, 2018 at 20:14
  • $\begingroup$ @Acccumulation Was just about to post that. Springs, iirc, give inconsistent amounts of power over the course of their life. We have many grandfather clocks, and I think only one is spring powered. They aren't unheard of, but they certainly aren't the norm. $\endgroup$
    – Carcigenicate
    Commented Feb 9, 2018 at 22:20
  • $\begingroup$ @Carcigenicate Good spring-driven clock have things called 'fusees' whose purpose is to even-out the force from the spring. Weight-driven clocks, like most long-case clocks, don't need these. $\endgroup$
    – user107153
    Commented Feb 10, 2018 at 0:31
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    $\begingroup$ "[The pendulum] is being driven by an oscillating magnetic field from the fixed magnet." If it's being driven by a fixed magnet, then that's a perpetual motion machine. The point is that it's an electromagnet. $\endgroup$
    – David Richerby
    Commented Feb 10, 2018 at 10:09
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    $\begingroup$ @DavidRicherby they mean fixed as opposed to the one moving on the pendulum. Fixed in space, not in magnetic strength. $\endgroup$
    – Tim
    Commented Feb 10, 2018 at 13:12
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The pendulum's weight and length combine to regulate the clock mechanism's swing duration or "speed." Your clock's energy is provided by battery power. Some of this energy is also being used to "power" the pendulum's electromagnetic. Because the pendulum's swing energy is provided every swing from the battery, your clock is operating in harmony with regard to the Laws of Thermodynamics.

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