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Vertical Pendulum Seismometer

A classical pendulum seismometer consists of a spring, a mass (black), and a damping device (light orange). These are all connected to a rigid frame that is fixed to the ground. When the ground moves, the mass is not able to move exactly in sync because of the inertia of the mass. The differential movement between mass and frame is recorded as a seismogram. The amplitude and phase differences between true ground motion and relative mass motion depend on the damping constant and the ratio of the frame-motion frequency to the eigenfrequency of the seismometer. The plot on the right shows these differences with the black dot indicating the current mass position.

Contributed by: Frank Scherbaum and Nicolas Kuehn

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Seismometers are the key tool in studying earthquake sources and the Earth's interior using seismic waves. In its simplest form, a seismometer consists of a moveable mass attached to a rigid frame by a spring and a damping system. The relative movement

of the mass with respect to the frame is recorded as a seismogram. Its relation to the true ground motion

is given by the seismometer equation

where

is the damping term and

is the eigenfrequency;

is the friction coefficient,

is the spring constant, and

is the attached mass;

is called the damping constant. Dependent on the values of

and the input frequency, the movement the mass experiences differs in amplitude and phase from the motion of the frame. For input frequencies close to the eigenfrequency of the system and small damping constants, the system exhibits resonance.

Reference:

F. Scherbaum, Of Poles and Zeros: Fundamentals of Digital Seismology, 2nd ed., Norwell, MA: Springer, 2007.

Damped Simple Harmonic Motion (Wolfram MathWorld)

"Vertical Pendulum Seismometer" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/VerticalPendulumSeismometer/

Contributed by: Frank Scherbaum and Nicolas Kuehn

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