Rott’s Pendulum
What to do: Twist the knob to set things in motion, then let go.
What happens: The two connected parts of the "pendulum" swing in
a totally chaotic and unpredictable fashion.
2 seconds
HOW IT WORKS
1. Rott's pendulum is really two pendulums coupled together.
The L-shoped one is pivoted in the middle or its long side; the short
pendulum hangs from the top of the "L". The side pendulum swings to
and fro in 1 second, the entire pendulum (when the side pendulum is not
swinging) takes exactly twice as long. This makes it very easy for
energy to transfer from one pendulum to the other, as their swings
coincide every two seconds.
1 second
2. For small swings, the pendulums behave predictably - try it out.
Energy is exchanged from one pendulum to the other at a steady rate
until friction makes them stop. However, for large swings, the
pendulums behave very erratically. They still interchange energy, but
swing, stop, and whirl round in an unpredictable fashion.
one or the other swings
3. The pair of pendulums is, in fact, a
"chaotic" system, whose motion cannot be
mathematically predicted, even if you know
the "initial conditions" very precisely; i.e.
how fast the two parts are turning round
and their positions when you let go of the
knob. The tiniest change in the initial
conditions (as well as the tiniest disturbance
during the motion) results in an entirely
different subsequent motion - not initially,
but at some critical time when the
pendulums stop or change direction.
DID YOU KNOW?
● The inventor of the pendulum, Nicholas Rott
is a retired physics professor living in
California.
STUART STREET
CARDIFF
CF10 5BW
whirling
4. These "critical points" are when one of the
pendulums reaches the top of a circular
swing and almost stops there. With a tiny
bit more swing, it will continue and swing
over the top; with a bit less, it will stop and
swing back again. Whichever of these things
happens only depends on a tiny difference
of energy of the pendulum, but massively
affects what the pendulum does
afterwards. You can be certain that the way
the pendulum behaved when you just set it going
with large swings will never be repeated, however
long the exhibit may last!
T 029 20 475 475
F 029 20 482 517
A critical
point.
Which way
will it go?
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