Drawing No. EH–CS–015 // Civil & Structural Engineering

Structural Resonance & Earthquake Oscillator Simulator

Reviewed August 2026

A building is a filter. Feed it ground motion at its own period and it amplifies; feed it anything else and it barely notices. Change the natural period, the damping and the ground motion and watch the amplification, then see what a tuned mass damper and base isolation each do to the same problem.

Educational model. A single-degree-of-freedom oscillator under harmonic base excitation, plus a two-degree-of-freedom model for the tuned mass damper. Real ground motion is transient and broadband, not a steady sine, so the steady-state peaks here are a steady harmonic idealisation. The response-spectrum tab uses a finite-duration harmonic envelope for intuition; it is not a code spectrum or a spectrum computed from a recorded accelerogram.

Building on shaking ground

amplification when the periods match

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Parameters

Live readout

What to watch for

Only the ratio matters

Slide the building period through the ground period and the amplification climbs to a sharp peak at r = 1 and falls away either side. A building twice as stiff or twice as soft as resonance is comparatively comfortable — the danger is narrow and specific.

Damping is only useful near the peak

Compare 2 % and 20 % damping on the response tab. Far from resonance the curves almost coincide; at r = 1 they differ tenfold. Damping does not make a building generally stiffer — it removes one specific catastrophe.

Steady state overstates a real earthquake

The harmonic peak assumes the shaking continues long enough for full resonance to build. Real strong motion lasts tens of seconds, so the response spectrum is lower and broader than the steady-state curve — the spectrum tab shows both.

Soft soil moves the target

Deep soft deposits lengthen the dominant ground period, which is why mid-rise buildings on soft basins suffer disproportionately. Raising the ground period on the spectrum tab moves the peak straight into the range of taller buildings.

A damper splits one peak into two

On the TMD tab, watch the single tall peak divide into two lower ones as the mass ratio rises. That splitting, not extra damping, is the mechanism — and it works only near the tuning frequency.

Isolation moves the building, not the earthquake

Base isolation pushes the period out to two or three seconds, far from where most seismic energy sits. The cost appears as displacement at the isolation plane, which is why isolated buildings need a moat.

Sources and technical basis

Single-degree-of-freedom base-excitation theory, with the standard Den Hartog tuning for the damper.

OpenStax — University Physics Volume 1Oscillations, damping, forced oscillation and resonance.USGS — earthquake hazards and ground motionGround-motion characteristics, site effects and how response spectra are used.NIST — earthquake engineering researchReference material on structural response, damping and seismic protective systems.