We will record the Poincaré section on the storage oscilloscope. Our first step is to adjust the optical detectors so that the axis for a purely planar vibration is well aligned with one of the optical detectors. Next, the signal from this optical detector is sent to one of the input channels of the oscilloscope. The other channel is used to record the velocity, via the differentiator, of this same signal. Lastly, the time-base on the oscilloscope must be set to X-Y mode, thereby allowing both the horizontal and vertical oscilloscope sweeps to be controlled by the external signals.
The result, as shown schematically in the oscilloscope in Figure 3.22, is an experimental rendering of the phase space trajectory for a string.
Figure 3.22: Schematic for the construction of an experimental Poincaré map
for the string apparatus.
To construct a Poincaré map, we need to sample this trajectory once each forcing period. That is, instead of recording the entire trajectory, we only want to record a sequence of points on this trajectory. This can be accomplished by turning the oscilloscope's beam intensity on for a brief moment once each forcing period. This is easy to do because on the back of most oscilloscopes is an analog input line labeled ``z'' that controls the oscilloscope's beam intensity. Finally, we need a triggering circuit that takes as input the sinusoidal forcing signal and generates as output a clock pulse, which is used to briefly turn on the oscilloscope's beam once each forcing period.