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π Seismic Response Explorer
A single-degree-of-freedom structure subjected to a ground motion pulse. Change the structure's natural period and damping ratio, and watch how its displacement response over time changes shape and magnitude β no score, no target, just a feel for why period and damping matter so much in seismic design.
Structure Properties
Ground Motion Pulse
Live Response
Peak displacementβ
Ductility demand proxyβ
Tn / Tp ratioβ
Response trendβ
This simulation runs the exact same Newmark-Ξ² time-integration
solver (
engine/dynamics.js β sdofNewmark) used in the SDOF
response calculators elsewhere on this platform. This engine was found to have
a real coefficient bug during this session's verification work (an incorrect
mass term caused up to 69% error against an independent Duhamel-integral cross-check on
another page) β it was fixed, then re-verified against a closed-form step-load case
(DLF=2.0, exact) and an independent scipy RK45 numerical integration (matching to
<0.03% at well-conditioned points). See tests/dynamics.test.js for the
full record.Method
ModelSDOF system under base excitation, integrated by Newmark average-acceleration (Ξ²=ΒΌ, Ξ³=Β½), unconditionally stable (Chopra Β§5.3).
PulseA single-cycle sine ground acceleration pulse β a simplified, illustrative "earthquake-like" input, not a real recorded ground motion.
Observed behaviorFor this single-cycle pulse, peak response increases roughly monotonically as Tn/Tp grows (a swept check from 0.2 to 2.8 showed no peak-then-decay). This differs from steady-state harmonic resonance, which does peak sharply near Tn=Tp β a genuine distinction between shock/pulse response and sustained-forcing resonance (Chopra ch.4 on shock spectra).