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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+