- Choose length = 1 m,
damping = 0.1 sec-1, and
amplitude = 0.07 m. Start with an initial condition of roughly 10°
and observe the behavior for different values of the frequency between
0.2 Hz to 1.2 Hz. In most cases, the initial oscillation dies out
except for values around 1 Hz where the down-hanging equilibrium is no longer
stable. Note, that the frequency of the excited oscillation is half the frequency of driving.
- Choose length = 1 m,
damping = 0.1 sec-1,
amplitude = 0.07 m, and frequency = 0.8 Hz.
Depending on the initial condition, you will get either a strong oscillation or
the oscillations decay to zero. Parametrically excited oscillations.
- Choose length = 1 m,
amplitude = 0.3 m, frequency = 3 Hz,
and arbitray nonzero damping.
Start with an intial condition near 180°. You will find that the upside-down
pendulum is no longer unstable. Why?
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