- What happens if the amplitude of driving is set to zero? How does the
behavior depend on the length and on the damping? Choose, for example,
length = 4 m. Now, compare the behavior for damping less
than and greater than 3.13 sec-1.
- Choose length = 1 m,
damping = 1 sec-1, and
amplitude = 0.2 m
(this are the default settings when the applet is started). Now, change the
frequency of driving very slowly from 0.2 Hz to
0.8 Hz. Observe the change in the amplitude of oscillation.
You can measure it by using the oscilloscope.
- Choose length = 1 m,
damping = 0.4 sec-1,
amplitude = 0.2 m and frequency = 0.4 Hz.
Depending on the initial condition, the pendulum oscillates either with a
large amplitude or with a small one.
- Choose length = 1 m,
damping = 1.566 sec-1,
and frequency = 0.3323 Hz. On the oscilloscope select the angle as the x-axis and the
angular velocity as the y-axis. For the scaling of the axes choose 180 and 500, respectively.
Now, switch the oscilloscope on and investigate the behavior for
the following values of the amplitude: 0.9 m, 1.07 m,
1.15 m, 1.35 m, 1.45 m, 1.47 m, and
1.5 m. You will observe simple periodic orbits,
period-doubling bifurcations and deterministic chaos.
Note, that with this sequence of the amplitude you will reproduce Fig. 3.4 of
in Baker and Gollub's book.
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