## PSN-L Email List Message

Subject: more horizontal seis boom angle
From: S-T Morrissey sean@...........
Date: Wed, 16 Feb 2000 13:21:07 -0600 (CST)

```Jack,

I believe that what I said and what you said are correct: if the boom
is horizontal, the hinges must be vertical. This, of course, is in
describing the horizontal pendulum configuration, also called the
"garden gate" design, as is the Lehman horizontal seis. This is the
common configuration for classic long-period horizontal seismometers,
as well as some modern broadbands such as the STS-1. (Other VBBs use
an inverted pendulum design, where the hinge is horizontal and at
the bottom of the boom, the boom is vertical, and the mass is at the
top: the hinge provides some restoring force, but with a practical mass,
this is inherently unstable, but OK for a fedback instrument).

Regarding Steve's question about the angles:

For simplicity the horizontal pendulum has always been designed so
that the boom and the hinge axis (either upper/lower pivots or more
continuous flexures) are at right angles. This then makes the angle
of the boom with respect to the horizontal the same as the angle of
the axis of rotation with respect to the vertical, so only one variable
angle is involved, which greatly simplifies the mathematical description
of the pendulum. The angle of the boom and therefore the period can then
be adjusted by tilting the base or frame along the axis of the boom, which
is usually an external adjustment so the cover does not have to be removed.
(The boom is often also designed to be parallel to the base or frame, which
facilitates the alignment of magnets, coils, and transducers.)

However, Since the boom or axis angle is small, sine(i) = i (radians),
and the natural period Tn = 2*pi*sqrt(L/(g*i)). As i gets very small,
the period gets very large. Actually, there is usually a small restoring
moment from the hinges or pivot wires, so the boom may stay at equilibrium
even if perfectly level. Obviously, if the mass end is raised up
so that the boom slopes down toward the lower pivot, it will flop over
to one side. At the other extreme, if the boom is vertical and hangs
straight down from the hinges, it is a simple pendulum, as in the SG design.

Regards,
Sean-Thomas

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