Re: Midterm Question - Sort of

[brian whatcott <inet@INTELLISYS.NET>]

At 22:12 7/6/99 -0500, you wrote:
> ...We can pump the swing by pushing on
> the child with that period, but we can also push every second time they
> come back (twice the period half the frequency)
> ... is it really accurate to think of this as multiplying the
> pumping frequency?...
> Doug Craigen

In the days of my youth, there was a watchmaker's shop with a
pendulum clock facing the street. There was a little brass
plaque explaining the operation of the pendulum.

This clock was something like a free-pendulum clock - which was
the height of the clockmaker's art at some time.
  When the arc of the pendulum decayed sufficiently, a switch made
contact, a solenoid operated, and the pendulum received another kick.

It was clear that this impulse could occur at any sub multiple of
 the pendulum frequency - the sole requirement was that energy
be added at a suitable phase.

In electrical terms, a full wave rectifier produces a strong frequency
contribution at twice the input frequency.
 So a benefit of this arrangement is the easier smoothing available
from a capacitor which offers half the reactance at twice the frequency.

What evidently does not trouble Doug is the case where the pump
frequency is higher than the signal frequency.
 This is a feature of the parametric amplifier - where a difference
frequency (pump minus signal) offers a negative resistance
(and consequent gain) to the signal.

If I recall, the usual illustration for high frequency pumping is
also the garden swing.
  This time, the pivot point is driven at twice the natural frequency.
(But I'm sure there is a more intuitive case, that I can't presently
recall :-)


brian whatcott <inet@intellisys.net>
Altus OK