Seismic Frequency to Period Conversion
The relationship between natural frequency and natural period, with conversion formulas and worked values for common seismic frequencies.
Relationship
Natural frequency (f) and natural period (T) are reciprocals. Frequency is measured in hertz (cycles per second) and period in seconds (time per cycle). The conversion is: T = 1 / f and f = 1 / T. Angular frequency (omega) is related by omega = 2*pi*f = 2*pi/T. In seismic analysis, frequency is used for spectrum lookup and period is used for code-based formulas and spectral shape characterisation.
Common values
| Frequency (Hz) | Period (s) | Angular frequency (rad/s) | Typical context |
|---|---|---|---|
| 1 | 1.000 | 6.283 | Flexible building fundamental mode |
| 2 | 0.500 | 12.566 | Mid-rise building |
| 5 | 0.200 | 31.416 | Stiff building or equipment on flexible floor |
| 8 | 0.125 | 50.265 | Equipment cabinet fundamental mode |
| 10 | 0.100 | 62.832 | Stiff equipment frame |
| 15 | 0.067 | 94.248 | Local panel or component mode |
| 20 | 0.050 | 125.664 | Local vibration mode |
| 33 | 0.030 | 207.345 | Rigid response boundary (typical) |
Notes
- The rigid-flexible boundary is often taken at 33 Hz (T = 0.030 s) but varies by standard
- Some standards define the rigid boundary at the frequency where the spectral acceleration equals the zero-period acceleration (ZPA)
- Angular frequency is required for converting between spectral acceleration, velocity and displacement