Fourier
Problem
Problem
Freq4P06
Name_______________________________________
Dr. Abner Mallity has been working with the Highway Department of the great
state of Utaho. Shown below is a recording of vibration data taken
from some strain gages on one of their bridges. They are concerned
that there might be strong resonances in this particular bridge.
(The strong resonances in "Galloping Gertie" comes to mind, although those
resonances were excited by wind, not traffic as in this case.) Here
is a typical data set.
Here is an expanded version
of the signal, and it does look like There is a periodic signal - indicative
of a resonance - in the data.
For the record, you
need to know this about the signal.
-
The signal record length
is 500 milliseconds (i.e. one half second).
-
The sampling interval
is 1 millisecond, so there are 500 points.
Dr. Mallity has taken the FFT of the signal, and that's shown below.
(It's a magnitude plot.) (Oh, and he did this in Mathcad, so the
smallest index is 0 - not 1 like in Matlab.)
Dr. Mallity notices that
there are serious spikes in the FFT, so he suspects that there might be
a periodic signal after all. He decides to magnify the horizontal
scale, and gets the plot below.
Answer the following
questions for Dr. Mallity.
-
Are there any resonances
in the bridge? (as evidenced by the presence of periodic signals)
-
If there are resonances,
determine the frequency of any resonance.