Jim,

As has been pointed out, the size of the mass is a determining
tradeoff in the design features that affect the noise of the sensor.
Bigger is better, but it really puts demands on the suspension and
base design. The largest comercial horizontal mass is in the 
Sprengnether S5100, which is 11 kg., requiring a massive cast aluminum
base and frame. This was meant to provide enough power output from
expected ground motions to drive a 90-second galvanometer for a long-
period photographic system magnification of 6000 at 30 seconds 
(which few stations achieved).

Modern fedback garden-gate horizontals have masses of less than 1 kg.
This is because little or no power is produced by the seis (dissipative 
damping is a noise source anyhow). A small mass reduces the demands
for strength and rigidity of the base and the suspension, expecially
the hinges or flexures.

The period of a horizontal seismometer is determined by the angle that
the boom makes with the horizontal, assuming that the restoring forces
of the suspension are minimal.

The natural period: Tn = 2*pi*sqrt(L/(g*sine i))
 
where L is the boom length in cm, g=980cm/sec^2, i is the angle
that the boom makes wrt the horizontal; (if i is measured in radians,
i is small, sine i = i). For example, a 40 cm boom hanging vertically
as a simple pendulum ( an angle of 90 degrees) has a period of 
1.3 seconds. (a one second clock pendulum is 24.8 cm). When tilted
horizontally to about 4 degrees, the period is 5 seconds. At
about a 1 degree angle, it is 10 seconds, and at about 0.23 deg.
it is 20 seconds. So the period is changing with inverse of the
square root of the angle, which is why long periods are so unstable.
But unstable also means sensitive to smaller ground motions.

Note that the size of the mass is not involved.o

In setting up a horizontal seismometer, the boom is usually set
parallel to the base, which is leveled. This is the infinite-period
situation; then the front or mass end of the baseplate is lowered
as the period is measured by timing several oscillations until
a reasonable period is achieved.

Regards,
Sean-Thomas

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