Any object that can vibrate freely will do so at a particular frequency that is called its ‘natural frequency’.

A building may be thought of as an ‘inverted pendulum’ with its lower end fixed to the ground and the upper end free to oscillate.

Every building has its own natural frequency of oscillation. The taller the building, the lower this frequency becomes. A 10-storey building typically oscillates with a frequency of around 1Hz, that is, it takes one second to complete one oscillation.

A building’s natural frequency may determine whether it sustains damage or not during an earthquake – if strong earthquake shaking happens to be at a frequency close to that of the building, a resonance phenomenon may set in, which could even cause the structure to collapse. It is therefore important to know how a building is likely to behave.

The natural frequency of a building is relatively easy to determine, by recording some minutes of horizontal ambient vibration at the top of the building and at the base.

The ratio of the amplitudes reaches a peak at a frequency equal to the natural frequency of the building.

The figure shows a number of ways in which a building may vibrate. The simplest, and most common, is the ‘fundamental’ mode of vibration.