Consider a variable frequency oscillator (or phase modulation).  Sometimes a 
frequency isn't either.
 
In your example (and mine) the "signal" is not characterized by a "frequency" 
(either cyclical or periodic, which I assert are the same).  It is best 
described, as the phase being some (unusual) function of time, and a 
non-constant derivative.  Some "signals" exist both electrically and on shafts.

--- On Wed, 3/25/09, [email protected] <[email protected]> wrote:

From: [email protected] <[email protected]>
Subject: [USMA:44112] Periodic Motion
To: "U.S. Metric Association" <[email protected]>
Date: Wednesday, March 25, 2009, 11:37 AM

John,

Consider the rotation of the wheels of a domestic vacuum cleaner in irregular
forward then backward motion.

Is the rotation of the wheels periodic motion?
There is no fixed point or fixed time interval.
Rotation is *sometimes* periodic motion, but not always.

"John M. Steele" <[email protected]> wrote:  
>...        
>   *Rotation is certainly periodic motion.              
>   Periodically, the same point on a shaft passes a     
>   fixed point of observation...

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