Why does the roof keep shaking?
Follow the red point at the base and the gold point at the roof. When the ground starts moving, the base follows first. The mass above tends to keep its previous motion, so columns and walls deform and pull the floors back.
A building has its own swaying rhythm. It may keep swaying after the ground stops. When repeated ground motion matches that rhythm, the swaying can build up. This is resonance.
Buildings of different heights and stiffnesses have different rhythms. Taller does not always mean more shaking. Damping carries away some vibration energy and reduces the motion.
A tall ruler building and three shakes
- Build a “tall building” from blocks or card, fixed to a board. Shake it slowly and evenly—it mostly follows along.
- Shake fast with small strokes—it cannot keep up either.
- Now find the rhythm that makes it swing bigger and bigger—that is resonance. Try a taller, softer building: the resonant rhythm has moved.
Note: real seismic design relies on the whole structural system, not dampers alone; the linear model never cracks or collapses.
Base excitation, resonance and damping
More: a closer explanation
Track two points: the terracotta dot at the foundation and the gold dot on the roof. When the ground accelerates, the base is carried along first; the floor masses resist the change through inertia, the columns shear, and the roof lags behind. Mass supplies inertia; the bending of columns and walls supplies the restoring force. A building is a vibrating system that stores and returns energy.
Give the base one short push and hold still: the building keeps swaying at its own rhythm. The time between successive roof peaks is the first natural period, set mainly by mass and stiffness. If the ground shakes near that rhythm, every push arrives at an effective moment and the response grows cycle by cycle—resonance. Damping caps the amplitude and carries the energy away.
Different buildings have different periods: short stiff ones respond more to fast shaking, tall flexible ones to slow. No height is always the most dangerous—the verdict depends on matching between the ground’s rhythm and the structure’s period.
Open: from one storey to many
A single-storey building is an oscillator under base excitation:
x is the displacement relative to the foundation; the absolute displacement is x + u_g. A multi-storey shear building treats each floor as a mass and each storey of columns as a stiffness, producing a matrix problem whose first mode and period shape the overall response.
Open: what damping does
Dampers do work on relative motion: the larger the velocity difference across them, the larger the resisting force, converting mechanical energy into heat. A bigger damping ratio ζ lowers the resonant peak and speeds the decay; real seismic safety still needs strength, ductility, detailing and site assessment—one damper solves nothing alone.
Limits of the model
The model covers two-dimensional, fixed-base, linear-elastic horizontal motion only. It does not predict cracking, collapse, yielding, torsion, vertical motion, soil–structure interaction or liquefaction. Real earthquakes mix many frequencies over a finite time—the response belongs to the ground and the structure together, and any claim that “some height is always worst” must first ask: for which building, and which record?