The amplitude, B, has a maximum value when
. This is called the
resonance
condition. Note that at resonance, B, can become
extremely large if b is small. (In the diagram at
right
is the natural
frequency of the oscillations,
, in the
above analysis). In designing physical systems it is
very important to identify the system's natural
frequencies of vibration and provide sufficient damping
in case of resonance. This clearly did not happen
in the design of the
Tacoma
Narrows Bridge (
Tacoma
Narrows Newsreel) in 1940.