Inertial recorder: seismogram (2D)

A seismometer is a mass on a spring with a damper. When the ground accelerates, the mass lags behind and its displacement relative to the frame is the signal: x'' + 2 zeta w0 x' + w0^2 x = -a_ground. Driven at frequency w the steady amplitude is a0 / sqrt((w0^2 - w^2)^2 + (2 zeta w0 w)^2), peaking near the natural frequency; below it the instrument is a flat accelerometer, above it it measures ground displacement. Free vibration decays as e^(-zeta w0 t) with logarithmic decrement 2 pi zeta / sqrt(1 - zeta^2).

What this 2D view adds

• The mass-spring-damper side view and a scrolling strip chart of displacement and ground acceleration.
• The amplitude and phase response against ground frequency (with the current drive marked) and the free-decay envelope.

Honest simplifications

One horizontal degree of freedom, linear spring and viscous damping, and a synthetic quake wave packet. Same integrator and parameters as the 3D page.