The natural frequency of a building is the speed at which it sways back and forth when it is pushed. A tall building will sway or rock back and forth as a result of wind and in tall buildings you can see water in the sink rock back and forth opposite the motion of the building.
The subject of natural frequencies is much more complicated but this is the essence of how they act.
You know when you whack a tuning fork and it vibrates at a specific frequency? That is the tuning fork's "Natural frequency". Well it's the same for buildings. If you excite a building with wind or an earthquake it will naturally vibrate at a certain frequency just like the tuning fork. Of course a building has a much lower frequency than a tuning fork...
Think of it as the frequency of free vibration. If you grab your car ratio antenna, move it, and then let it go, it will vibrate at a certain frequency and with a certain shape. This frequency and shape would be very close approximations to the natural frequency and natural mode shape.
A structure has many natural modes. Often, the one with the lowest natural frequency is the main one we care about, but not always. In my car antenna example, that frequency and shape would be just one of the natural modes.
If a structure is pushed at a certain frequency, it vibrates at that excitation frequency, not the natural frequency--need to keep that straight.
time it takes to get from one extreme to the other. like a building moving from one max deflection in one direction to the max deflection in the other direction. or that's the period. well, then it's the inverse of the period.
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