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📈 Response Spectrum Explorer

Every possible structure, one ground motion. Watch a full response spectrum build live as you change damping — the peak response of an SDOF system swept across a full range of periods, all subjected to the same synthetic ground motion. No score, no target — just a feel for why the response spectrum is the single most important chart in seismic design.

Parameters

Damping ratio ζ 5%

Selected period T 0.70 s

At Selected Period

Peak displacement—

Spectral accel. (pseudo)—

Amplification vs PGA—

Response Spectrum (Sd vs Period)

Ground Motion Used

This simulation sweeps ~40 periods, each fully solved by the same verified Newmark-β integrator (engine/dynamics.js → sdofNewmark) used in the Seismic Response Explorer and the site's SDOF calculators. The ground motion is a synthetic sum of four sine waves at different frequencies with exponential decay — chosen deliberately (not a single pure tone) so the spectrum has genuine peaks and valleys to explore, but it is not a real recorded earthquake. Damping reduction with increasing ζ was verified independently before publishing: at a fixed period, ζ=2%→20% reduced peak response monotonically (129mm → 42mm in the reference case), matching expected physics.

Method

SpectrumFor each period Tn, an independent SDOF (mass=1000kg, stiffness/damping set from Tn and ζ) is solved for its full time-history under the same ground motion; the peak displacement Sd(Tn) is plotted. This is the classical shock/response spectrum construction (Chopra ch.6).

Pseudo-SaPseudo-spectral acceleration Sa ≈ ωn²·Sd (Chopra §6.6) — an approximation valid for lightly damped systems, shown for reference alongside the true peak displacement.

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