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[Phys-l] frequency modulation : f(w t) ... or not



Here's a little morsel that recently renewed its acquaintance with me.

A lot of people are accustomed to writing periodic functions in the
form f(w t). If the frequency w is constant, that's fine ... but
otherwise it's a trap for the unwary.

In general, you almost certainly want the argument of f() to be
integral w dt
which is equal to
w t
if w is constant, but generally not otherwise.

For additional discussion of this point, including a diagram, see
http://av8n.com/physics/rotating-frame.htm#sec-fm

I hope most people consider this obvious ... but I thought I'd mention
it anyway, because I've seen smart people get badly fooled by this.
On a couple of occasions I've seen large-ish /groups/ of smart people
completely flummoxed by this.

This issue comes up in connection with rotating frames: There is a
omega_dot (i.e. theta_dot_dot) term that shows up if you consider
unsteady rotation. Most textbooks ignore this term, but it's easy
to include it if you want to.

This issue also comes up in many other contexts, including obviously
FM radio electronics and signal processing.