## PSN-L Email List Message

Subject: Re: 30 second period
From: Brett Nordgren Brett3mr@.............
Date: Tue, 18 Dec 2007 17:19:18 -0500

```Ted,

At 12:17 PM 12/18/2007 -0700, you wrote:
>Hi Folks,  I will leave my Band Saw Blade sensor set up until I record a
>few earthquakes, just to see how they look.  Meanwhile the sensor is in
>the garage and is picking up a lot of noise, both from the road
>construction, near by, and me moving around the garage.   However it all
>quiets down at night.
>
>After this test, I do wish to pursue the idea of using music wire, piano
>wire, or the like.   I also will secure both the top and bottom of the
>wire, and put the barbell in the center.
>
>Before I make the next device, could someone answer these questions.
>
>1.  I know the shorter the wire the shorter the period, but If I use two
>wires, say 36", one on top of the horz and one on the bottom of the horz,
>would the period be the same as using one,
>72" wire, on the top only?   Or would it just reflect the length of the
>top wire only, and not the bottom wire?

At first glance, I think the period would become 1/2 that of the
original.  The spring constant (or more properly the torsion coefficient,
which is defined as the change in torque / change in angle) of each 36"
spring would be twice that of the 72" and also, the total spring constant
would be the sum of the upper and lower wires, making the total
coefficient  = 4X the original.  The free period is the sqrt(mom of inertia
/ torsion coefficient) so after splitting the wire the period would be 1/2
the original.

>  2.  Using the same mass and length of wire, would thinner wire result in
> a longer period?

Yes, since the period is proportional to 1/sqrt(torsion coeff).   For a
given wire material, the torsion coefficient is proportional to Dia.^4 /
Length.  So cutting the diameter in half, reduces the torsion coefficient
by a factor of 16, and so increases the period by a factor of 4.  Note that
doubling the length only increases the period by a factor of about 1.4.

>  3.  This was a surprise:  As I mentioned, the isolation continued for
> 5hrs.   I have tried different pendulums, with different hinges.  I have
> tried different springs.  These would only cycle for a few seconds and up
> to maybe 30 mins.   Can someone explain the different, of the longer
> periond of the torsion spring?

It turns out that the two types of pendulums would be measuring different
things.

Any motion, including the motion of a point on the earth, can be completely
described by six parameters, three translation, straight-line motions:
up-down, East-West, North-South, and three rotational motions: around a
vertical axis, a N-S axis and an E-W axis.  Seismographs normally measure
the translations because for earthquake generated motion, they are usually
much larger than the rotations.  Early in the history of seismographs, as I
recall, there was a debate going on whether horizontal pendulum designs
were recording mainly translation or were also measuring
rotation.  Translation won.

Some earthquake phases have both translation and rotation, which I believe
are related to each other by the wavelength.  For typical wavelengths
through the ground, translation is usually much the larger effect, though
your experiments are showing that it may be much easier to make a good long
period torsion device than an equivalent regular pendulum.  It might be
that you could get useful results recording the much smaller rotations
(about the vertical axis), simply because it was easier to make a much
better torsion pendulum.

Hope this helps,

Brett

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