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Re: "simple" pendulum



THE MESSAGE BELOW WAS TYPED OFF-LINE. THEN I
FOUND THAT JOHN AND JACK ALREADY ADDRESSED
THE ISSUE OF SIMPLICITY. WAS MY SLEEPING BRAIN
PICKING THE EKG SIGNALS GENERATED BY THEM?

What do conical and simple pendula have in common?
Provided L is the same, the motion of the bob is confined
to the same sphere. But in one case it is a constant THETA
while in the other it is a constant PHI (spherical coordinates
in a system whose origin is at the suspension point and whose
axis is vertical).

In both cases the restoring force is due to gravity. But in a
conical pendulum that force has a constant magnitude, only
its orientation is variable. In the simple pendulum, however,
both the magnitude and the direction are time dependent. That
is why a conical pendulum (provided trajectories are circular)
is more simple than its flat cousin. One does not have to write
F=m*a as a differential equation in order to derive the formula
for T (see the last message from Leigh). Elliptical trajectories
of the suspended bob (when both THETA and PHI are variable)
are the most complicated. Nothing profound, just pondering
on another misconception.

There is much more in this, mathematically, than I can grasp,
but that is another story. What else is new?
Ludwik Kowalski