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A mechanical phase locked loop!
On 05/08/17 20:14, Gareth's Downstairs Computer wrote:
On 05/08/2017 20:06, rickman wrote: Yes, because it *is* a PLL. In fact the problem most people have with it is that it doesn't adjust the phase by adjusting the frequency of the slave. It adjusts the *phase* so clearly it *is* a phase locked loop. All pendulums have circular error where the frequency is determined by the amplitude of swing, so for the half cycle where the phase is adjusted by abridging the swing by the hit of the hit and miss stabiliser, the frequency of the slave is, indeed, changed. The standard formula given for the cycle time of pendulums .. 2 * PI * root( L / G) ... is only valid for those small angles where sin( theta ) = theta, and such angles are so infinitesimal that no visible movement of a pendulum would be seen! You seem to be confusing two different things The error you refer to is due to the pendulum not actually taking a direct line between the ends of its travel, the error is small for small amplitudes. There was a famous experiment by a Frenchman in, I think Paris, he hung a huge pendulum and let it trace its path in sand, rather than it going 'to and fro' it actually went in arcs as it went to and fro. The effect is minimised by reducing the amplitude. As you correctly say, the frequency of a pendulum is given by the formula you state. If you 'give it a nudge' you may shorted one swing but the overall frequency is still determined by the formula. The 'nudge' will change the phase of the swing, not the frequency- ie it will shorten one cycle. |
#2
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A mechanical phase locked loop!
Brian Reay wrote on 8/5/2017 5:10 PM:
On 05/08/17 20:14, Gareth's Downstairs Computer wrote: On 05/08/2017 20:06, rickman wrote: Yes, because it *is* a PLL. In fact the problem most people have with it is that it doesn't adjust the phase by adjusting the frequency of the slave. It adjusts the *phase* so clearly it *is* a phase locked loop. All pendulums have circular error where the frequency is determined by the amplitude of swing, so for the half cycle where the phase is adjusted by abridging the swing by the hit of the hit and miss stabiliser, the frequency of the slave is, indeed, changed. The standard formula given for the cycle time of pendulums .. 2 * PI * root( L / G) ... is only valid for those small angles where sin( theta ) = theta, and such angles are so infinitesimal that no visible movement of a pendulum would be seen! You seem to be confusing two different things The error you refer to is due to the pendulum not actually taking a direct line between the ends of its travel, the error is small for small amplitudes. There was a famous experiment by a Frenchman in, I think Paris, he hung a huge pendulum and let it trace its path in sand, rather than it going 'to and fro' it actually went in arcs as it went to and fro. The effect is minimised by reducing the amplitude. I believe you are thinking of the Foucault pendulum. This had nothing to do with elliptical paths of pendulums. This was a pendulum free to swing along any axis. As the earth rotates the pendulum continues to swing in its original path and the earth turns beneath it. Of course the pendulum appears to rotate the plane of swing. As you correctly say, the frequency of a pendulum is given by the formula you state. If you 'give it a nudge' you may shorted one swing but the overall frequency is still determined by the formula. The 'nudge' will change the phase of the swing, not the frequency- ie it will shorten one cycle. Yes, that is right. The change in frequency (phase change rate) is only momentary. -- Rick C |
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