** Next:** Decreasing the restoring force
**Up:** Design of seismic sensors
** Previous:** Design of seismic sensors

##

Pendulum-type seismometers

Most seismometers are of the pendulum type, i.e. they let the mass
rotate around an axis rather than move along a straight line (Figs. 7 to 10;
the point bearings in our figures are for illustration only, most
seismometers have crossed flexural hinges). Pendulums are not only
sensitive to translational but also to angular acceleration. Since the
rotational component in seismic waves is normally small, there is not
much practical difference between linear-motion and pendulum-type
seismometers. However, they may behave differently in technical
applications or on a shake table where it is not uncommon to have
noticeable rotations.

For small translational ground motions, the equation of motion of a pendulum is formally identical to Eq. (25) but *z* must then be interpreted as the angle of rotation. Since the rotational counterparts of the constants *M*, *R*, and *S* in Eq. (25)
are of little interest in modern electronic seismometers, we will not
discuss them further and refer the reader instead to the older
literature, such as [Berlage Jr. 1932] or [Willmore, P. L. (ed.) 1979].

The simplest example of a pendulum is a mass suspended with a string or
wire (like Foucault's pendulum). When the mass has a small size
compared to the length
of the string so that it can be idealized as a point mass, then this is called a *mathematical pendulum*. Its period of oscillation is
where *g*
is the gravitational acceleration. A mathematical pendulum of 1 m
length has a period of nearly 2 seconds; for a period of 20 seconds the
length has to be 100 m. Clearly, this is not a suitable design for a
long-period seismometer.

** Next:** Decreasing the restoring force
**Up:** Design of seismic sensors
** Previous:** Design of seismic sensors
*Erhard Wielandt *

2002-11-08