Oscillations and Waves > Oscillations > Nonlinear Systems
 DCS# 3A95.50b
POINCARE SECTION


APPARATUS
Pasco nonlinear oscillator 202-13-F
DC power supply 202-08-D
laptop with LoggerPro
 206
LabPro interface 107-02-B3
photogate 202-14-C2
1/4" stereo jack to BTA adapter
 202-14-C1

DESCRIPTION
A rotary motion sensor is used to produce a phase plot and a Poincare plot for a damped driven physical pendulum undergoing chaotic motion.  Both graphs show the pendulum's angular speed vs angular position but, for the Poincare plot, points are recorded only once per drive cycle, when the driver passes through a photogate.  The graph shown above represents 50-minutes-worth of data.  Data collection is set to run for 50 minutes, but can be set to continue overnight, or longer.

NOTES
Set up nonlinear oscillator in the usual manner.  Position photogate so driver passes through it once each cycle.

Adjust frequency for chaotic motion.

Use LoggerPro 3 "poincare" experiment file.

Settings are:
ch1 = raw voltage:  to read photogate voltage
digital input 2 = rotary motion sensor/angular/high resolution
experiment length =  6000 sec
sample rate = 30 pts/s
graph 1 = angular speed vs angular position
graph 2 = ang velocity at constant phase vs angular position at constant phase

Check measured photogate voltage and, if necessary, modify values in constant phase definitions.

Zero rotary motion sensor with edge mass at the top of the disk.

The points at the origin are artifacts resulting from the method used for obtaining a poincare plot from the rotary motion sensor data.
nonlinear oscillator

The continuous ω vs. θ data eventually fills the phase space:


after 5 minutes: 


after 60 minutes: 

This is available for use in the display case.