Response to Sinusoidal Ground Motion: Beats, Resonance and Phase

Run a Computer Simulation
To see the beat phenomenon first hand, you can run the computer simulation without damping and without a sine sweep. If you use frequency equal to a floor's natural frequency, it will be especially noticeable in that floor. (You can use the calculator on the previous page to find a natural frequency)

If the ground motion is sinusoidal, the building will eventually oscillate at exactly the same frequency as the ground motion. As the building approaches this single-frequency response, it may oscillate at one or more of its natural frequencies. If the ground motion frequency is close to a natural frequency, then the building may oscillate at both the ground motion frequency and the nearby natural frequency. At some instants in time the two responses will add together, while at other instants in time, the two responses will cancel each other out. The net effect of the sum of two oscillations of nearly the same frequency is a beat phenomenon in which the oscillation appears to have a frequency which is equal to the average of the two individual response frequencies, and in which the amplitudes grow and decay over several periods of the response, as shown below in Figure 7.

Figure 7: The beat phenomenon occurs when two oscillations of nearly the same frequency are superimposed.