From: ChrisAtUpw@.......

Date: Thu, 28 Nov 2002 21:25:22 EST

In a message dated 28/11/02, rpratt@............. writes: > Refering to earlier. > > May I suggest an experiment for the proponents of the ball? Operate with > as > > little damping as possible and compare to a true sine wave equally damped. > > It may be easier to just measure 1) the period and 2) the damping > factor. The damping gives an exponential fall off in the amplitude of the > oscillation. These should be easy to do using your A/D logging program. > > I wasn't thinking of just period and damping. My thought was that if the > pivot axis is changing toward a more stable configuration (different sized > ball pivots or no upper ball) the pure sine wave will be deformed by a > higher restoring force with an increase in displacement and provide > experimental evidence for ball pivots being more stable at least in the > Hi Randy, I should have explained my suggestions more fully. Even if the suspension system is not quite linear, the difference that you will see on the real pendulum motion by comparing it to a sine wave, will be tiny. Simple pendulums also show small deviations from pure sine wave due to sin(angle) being assumed to be = angle. Trying to observe deviations directly on the waveform, particularly when the amplitude is changing, is a 'non starter'. I suggested two measurements that may react to the averaged effects and might be more helpful. The distortion that will occur will be mostly third harmonic. You have two possible sources. One is the pendulum itself and the other is non linearity of the sensor response. If you had a very linear sensor system, you could set the seismometer up for say 6 sec oscillations and look for signals of 2 sec period, but the usual coil + U magnet systems are likely to generate far more distortion than the pendulum! You could try putting the coil output into a twin Tee filter set to reject the natural pendulum frequency and then amplify the remaining signal. You can get ~55 dB rejection this way from a single filter, so deviations of a few parts in 1000 will show up and you can watch the decay in real time with a 'scope. We need a suspension system which has minimum natural damping, minimum hysteresis and more importantly, one in which the rotational axis is constant and very closely defined. Now how good is good? The period of a pendulum with an arm length L suspended with the rotational axis at angle A to the vertical is P = 2 x Pi x Sqrt(L / (g x sinA)). I visited Bob Barns' Website at http://mywebpages.comcast.net/ROYB1/ and he quotes a Teledyne Geotech SL-220 horizontal seismometer with an 8" arm attaining a period of 30 sec. g = 9.81 m^2/sec and L = 0.2 m. I fed this into the equation and A = 3 min of arc. Moreover, you have to be able to set this up reliably, so we are considering setup angles of just a few sec of arc. The suspension system also has to be rigid / stable to near this order. This is perhaps an extreme example and is obtained by the use of crossed foil suspensions, but see my previous EMails for A for pendulums with 25 and 100 cm arms. Meredith says that his Sprengnether with single wire suspensions and a boom length of ~ 15" between the coil sensor and the pivot area, does have a stability problem much over 15-20 seconds. Since this is a very rigid seismometer, it may well be the wire suspension which is the limiting factor. Summing up, you may be limited in the period that you can set by the suspension system, or by the rigidity / stability of the apparatus, or by the stability of the local ground. It would be very interesting to make two seismometers identical in all respects except for the suspension systems and compare the damping and the limiting periods. I suspect that the limiting periods of 'traditional' systems could be improved by additional bracing, since this would prevent changes in the support angle due to temperature changes. I hope that this answers your question well enough. Regards, Chris Chapman In a message dated 28/11/02, rpratt@............. writes:

Refering to earlier.

> May I suggest an experiment for the proponents of the ball? Operate with as

> little damping as possible and compare to a true sine wave equally damped.

It may be easier to just measure 1) the period and 2) the damping

factor. The damping gives an exponential fall off in the amplitude of the

oscillation. These should be easy to do using your A/D logging program.

I wasn't thinking of just period and damping. My thought was that if the pivot axis is changing toward a more stable configuration (different sized ball pivots or no upper ball) the pure sine wave will be deformed by a higher restoring force with an increase in displacement and provide experimental evidence for ball pivots being more stable at least in the extreme.

Hi Randy,

I should have explained my suggestions more fully. Even if the suspension system is not quite linear, the difference that you will see on the real pendulum motion by comparing it to a sine wave, will be tiny. Simple pendulums also show small deviations from pure sine wave due to sin(angle) being assumed to be = angle. Trying to observe deviations directly on the waveform, particularly when the amplitude is changing, is a 'non starter'. I suggested two measurements that may react to the averaged effects and might be more helpful.

The distortion that will occur will be mostly third harmonic. You have two possible sources. One is the pendulum itself and the other is non linearity of the sensor response. If you had a very linear sensor system, you could set the seismometer up for say 6 sec oscillations and look for signals of 2 sec period, but the usual coil + U magnet systems are likely to generate far more distortion than the pendulum! You could try putting the coil output into a twin Tee filter set to reject the natural pendulum frequency and then amplify the remaining signal. You can get ~55 dB rejection this way from a single filter, so deviations of a few parts in 1000 will show up and you can watch the decay in real time with a 'scope.

We need a suspension system which has minimum natural damping, minimum hysteresis and more importantly, one in which the rotational axis is constant and very closely defined. Now how good is good? The period of a pendulum with an arm length L suspended with the rotational axis at angle A to the vertical is P = 2 x Pi x Sqrt(L / (g x sinA)). I visited Bob Barns' Website at http://mywebpages.comcast.net/ROYB1/ and he quotes a Teledyne Geotech SL-220 horizontal seismometer with an 8" arm attaining a period of 30 sec. g = 9.81 m^2/sec and L = 0.2 m. I fed this into the equation and A = 3 min of arc. Moreover, you have to be able to set this up reliably, so we are considering setup angles of just a few sec of arc. The suspension system also has to be rigid / stable to near this order. This is perhaps an extreme example and is obtained by the use of crossed foil suspensions, but see my previous EMails for A for pendulums with 25 and 100 cm arms. Meredith says that his Sprengnether with single wire suspensions and a boom length of ~ 15" between the coil sensor and the pivot area, does have a stability problem much over 15-20 seconds. Since this is a very rigid seismometer, it may well be the wire suspension which is the limiting factor.

Summing up, you may be limited in the period that you can set by the suspension system, or by the rigidity / stability of the apparatus, or by the stability of the local ground. It would be very interesting to make two seismometers identical in all respects except for the suspension systems and compare the damping and the limiting periods. I suspect that the limiting periods of 'traditional' systems could be improved by additional bracing, since this would prevent changes in the support angle due to temperature changes.

I hope that this answers your question well enough.

Regards,

Chris Chapman