- 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 and the change
in the phase between driving and pendulum oscillations.
You can measure it by using the oscilloscope.
| Related topics in the lecture room:
Resonance.
|
- Choose the parameters as above but now change the frequency between
3 Hz to 4 Hz. Observe a shift of the center of oscillation
either to the left or to the right (this is a pitchfork
bifurcation). This bifurcation does not occur for the
pendulum driven by a periodic force. Why not?
- Choose length = 1 m,
damping = 1 sec-1,
amplitude = 0.85 m, and frequency = 1 Hz.
You will observe an irregular motion called deterministic chaos
with a seemingly random number of left and right
turns. 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 1000, respectively.
Now, switch the oscilloscope on and you will be fascinated by the beautyful
curves drawn on the screen.
Turning the oscilloscope into a Poincaré map
by selecting external triggering in order to see the irregularity better.
|
elmer@ubaclu.unibas.ch
last modified Saturday, July 25, 1998.
