# In the absence of ALL friction, would a pendulum swing forever? **URL:** \ **Category:** Factual Questions\ **Created:** [February 15, 2008, 3:57pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749 "2008-02-15T15:57:24Z")\ **Posts on this page:** 13\ **Page:** 2
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 16, 2008, 6:35pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/21 "2008-02-16T18:35:00Z")
[QUOTE=Napier] \>It’s not right to assume that just because there is gravity there is gravitational radiation. For example I don’t think a massive object undergoing SHM produces gravitational waves in itself. Well, of course it is. I mean, it isn’t an assumption. Any change in a gravitational field propagates away from the matter that is creating the change, at the velocity c. If it propagated at any other speed, then it would be possible to define a real physical reference frame in which the effect caused by the change in the matter preceeded the cause itself, which violates causality. A massive object undergoing simple harmonic motion certainly changes the gravity field around it, including out to infinite distance, in this way. Even a massive object that is simply rotating in a sense in which it does not have rotational symmetry has to do this. [/QUOTE] I don’t see where you’re coming from. Just because the pendulum is moving does not mean it generates gravitional waves. I’m no expert on gravitational waves, but SHM can parameterized by 1 parameter which makes me suspect that no gravitational waves are being generated. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [February 16, 2008, 6:58pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/22 "2008-02-16T18:58:51Z")
[QUOTE=These are my own pants] It’s not right to assume that just because there is gravity there is gravitational radiation. For example I don’t think a massive object undergoing SHM produces gravitational waves in itself. [/quote] Any source with a time-varying [quadrupole moment](http://en.wikipedia.org/wiki/Quadrupole#Gravitational_quadrupole) will radiate some amount of gravitational radiation; this does in fact include an object in SHM. > [@](#): > > If I had to guess I’d say yes there probably is gravitational radiation as a high-order effect, but the actually effect would be almost incomphrehensively small. This statement is still correct, though. I just ran through the numbers, and I found that a 10-gram pendulum swinging back & forth with amplitude 1 cm at the end of a 30-cm pendulum radiates about 10[sup]-60[/sup]watts of energy in the form of gravitational waves. If it continued to radiate its energy only in this form, at this rate, it would run out of energy in just 10[sup]47[/sup] years. For comparison, this about 10,000,000,000,000,000,000,000,000,000,000,000,000 times longer than the current age of the Universe (give or take an order of magnitude.) ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [February 16, 2008, 8:15pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/23 "2008-02-16T20:15:29Z")
\>If it continued to radiate its energy only in this form, at this rate… Nicely done, MikeS! It wouldn’t continue to radiate at that rate, though. It would radiate at a rate that was proportional to the amplitude, so the amplitude would decay with a relaxation time of the time period you quote. Every 10^47 years, the amplitude would be smaller by the ratio 1/e. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [February 16, 2008, 9:00pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/24 "2008-02-16T21:00:46Z")
Tidal forces in the pendulum and the planet would eventually stop it. ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [February 16, 2008, 9:31pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/25 "2008-02-16T21:31:22Z")
[QUOTE=kanicbird] Tidal forces in the pendulum and the planet would eventually stop it. [/QUOTE] But wouldn’t that be called friction? And where in the OP does it say this pendulum is on a planet? ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [February 16, 2008, 9:41pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/26 "2008-02-16T21:41:26Z")
[QUOTE=Musicat] But wouldn’t that be called friction? [/QUOTE] Yes, I think it would, but then again you can have it converted to kinetic energy if the substance is water, or elastic and inelastic deformations are also possible, [QUOTE=Musicat] And where in the OP does it say this pendulum is on a planet? [/QUOTE] Well it has to be gravitationally bound to something, planet, star, moon, perhaps there would be no tidal forces if it was bound to a black hole in the black hole itself, though the tidal forces would still be in the pendulum. ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [February 16, 2008, 10:59pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/27 "2008-02-16T22:59:12Z")
[QUOTE=kanicbird] Well it has to be gravitationally bound to something, planet, star, moon, perhaps there would be no tidal forces if it was bound to a black hole in the black hole itself, though the tidal forces would still be in the pendulum. [/QUOTE] According to Einstein, acceleration and gravity are equivalent. It could be on an accelerating object which would not be subject to tidal or coriolis forces (or a planet not rotating about its own axis). I’m not sure what you mean by tidal forces. Do you mean the interaction between the object supplying the gravity and the pendulum, even if not physically touching? I interpret the OP to ask, “in the total absence of any other forces, subject only to the force necessary to cause a pendulum to cycle, would the cycle ever die out?” ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [February 16, 2008, 11:10pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/28 "2008-02-16T23:10:18Z")
[QUOTE=Musicat] According to Einstein, acceleration and gravity are equivalent. [/QUOTE] For a point only, gravity would act on 2 points slightly differently due to the distance and angle to the gravitationally bound object [QUOTE=Musicat] I’m not sure what you mean by tidal forces. Do you mean the interaction between the object supplying the gravity and the pendulum, even if not physically touching? [/QUOTE] The internal forces that developed inside both objects due to the gravitational force between them. The earth/moon is a example. The moon is however gravitationally locked, so any tidal force would be small and just tend to stabilize the lock (but still there). In the earth we have ocean tides which is caused by the gravity of the moon (the soild earth also has tides, but the oceans are easier to see), the tides are caused by energy ‘stolen’ from the earth-moon system causing a drag, a new energy loss as the energy is converted to kinetic energy of the oceans, then to heat through frictional losses. ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [February 16, 2008, 11:29pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/29 "2008-02-16T23:29:54Z")
[QUOTE=Public Animal No. 9] \ Beyond the hysteresis question, if the pendulum’s materials are real (except for the non-friction aspect), then the repeated alternating stresses will result in the pendulum failing due to fatigue at some point before “forever”. My guess is that would happen before it came to a halt due to the other factors. [/QUOTE] This would be true for a material such as titanium. However, other materials, such as steel, do not exhibit an endurance limit, and therefore, would not fail in the manner suggested. ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [February 17, 2008, 12:00am UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/30 "2008-02-17T00:00:58Z")
[QUOTE=MikeS] a 30-cm pendulum radiates about 10[sup]-60[/sup]watts of energy in the form of gravitational waves. [/QUOTE] This is getting down to the point where the occasional collision with a neutrino becomes significant. 0.000079 electron volts = 1.2657194 × 10^-23 watts second Unless you shield against neutrinos, the pendulum will swing chaotically, forever. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 17, 2008, 2:19am UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/31 "2008-02-17T02:19:34Z")
[QUOTE=MikeS] Any source with a time-varying [quadrupole moment](http://en.wikipedia.org/wiki/Quadrupole#Gravitational_quadrupole) will radiate some amount of gravitational radiation; this does in fact include an object in SHM. This statement is still correct, though. I just ran through the numbers, and I found that a 10-gram pendulum swinging back & forth with amplitude 1 cm at the end of a 30-cm pendulum radiates about 10[sup]-60[/sup]watts of energy in the form of gravitational waves. If it continued to radiate its energy only in this form, at this rate, it would run out of energy in just 10[sup]47[/sup] years. For comparison, this about 10,000,000,000,000,000,000,000,000,000,000,000,000 times longer than the current age of the Universe (give or take an order of magnitude.) [/QUOTE] Cheers 😃 General relativity is the most beautiful theory in physics by a mile. I suppose howver which way you frame it SHM does not occur in stationary spacetime. ---
**Author:** ![Mister\_Earl](https://avatars.discourse-cdn.com/v4/letter/m/ee7513/32.png) [@Mister\_Earl](https://boards.straightdope.com/u/Mister_Earl)\ **Post date:** [February 18, 2008, 5:51am UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/32 "2008-02-18T05:51:28Z")
You all are making me laugh. The OP asks for “basic physics help” and gets answers full of nuances of material science and quantum gravitational effects. Basically, in a classical sense, if there are no forces acting on the pendulum than gravity, it will swing forever. The amount of potential energy at the top of the swing, where the velocity is zero, is exactly the same amount of kinetic energy when the pendulum is at the bottom where the velocity is maximized. Each little bit of potential energy is traded into greater and greater velocity as the pendulum swings “downhill.” As it swings “uphill,” each little bit of kinetic energy is traded back to potential. At any one point the sum of the kinetic and potential energies is exactly the same. Since, by definition of the problem, there is no other force dissipating energy in the pendulum, it will swing forever. Of course, there is no way it could ever be built under any conditions, but the OP was asking about the basic relationship between velocity and gravity in a classical pendulum problem. ---
**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\ **Post date:** [February 18, 2008, 1:16pm UTC](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749/33 "2008-02-18T13:16:05Z")
Thanks,\*\* Mr. E.\*\* I had to deduce that from all the theoretical blah blah that followed my OP. That’s exactly what I was asking, and I thank you for answering it. I asked what time it was, and was told how to make a watch. [Previous page](https://boards.straightdope.com/t/in-the-absence-of-all-friction-would-a-pendulum-swing-forever/437749.md?page=1)