In article , Gary Coffman says...

But for a pendulum, the displacement
and the force are still orthogonal.

No it isn't.

OK, I was thinking of the force on the wire, holding up
the ball.

The gravitational force that causes it to oscillate
is pretty much vertical though, and pretty much
cancelled out by the force of the wire holding the
ball up.

The analysis of a pendulum that resolves into simple
harmonic motion *depends* on the wire being long,
so the restoring force away from the bottom of the
swing looks nearly proportional to the displacement
of the ball.

If the wire is short, or if the swing becomes long,
then really the restoring force looks proportional
to the *sine* of the displacement angle, and the
ball no longer displays simple harmonic motion.

Jim

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