Fourier transform and oscillation amplitude

Howdy mathematicians!

How can one obtain the oscillation amplitude from the Fourier spectrum?
This question is trivial if discrete Fourier transform has value
different than zero only for one frequency. However, usually Fourier
transform looks something like that:

6.0 Hz - 1 mm
6.1 Hz - 10 mm
6.2 Hz - 40 mm
6.4 Hz - 5 mm

What is the amplitude of oscillation in that case?

Also, if 40 mm represents a peak, what is a correct name the whole
structure? In physics we commonly use expression "mode", but I find
this expression rather clumsy for other disciplines.

Thanks for the answers,

Marko

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