PIRA 3A95.00 NON-LINEAR SYSTEMS

DCS #DEMONSTRATIONREFERENCEABSTRACT
3A95.00Non-Linear Systems
3A95.10water relaxation oscillatorPIRA 1000
3A95.10water relaxation oscillator33-1.4A cylinder is filled with water at a constant rate and periodically empties.
3A95.12electrical and water relaxation osc.AJP 39(5),575A water relaxation oscillator models a neon flasher relaxation oscillator.
3A95.13pipet rinser oscillatorAJP 40(2),360The commercial pipet rinser is a much better relaxation oscillator than that in AJP 39(5),575.
3A95.15wood relaxation oscillator3A95.15A wood block rides up and slides back on the inside of a turning hoop.
3A95.20wood block relaxation oscillatorPIRA 1000
3A95.20water feedback oscillator15-10.13A tubing and bellows arrangement to generate oscillations by feedback. Picture.
3A95.22compound pendulumAJP 45(10),994A driven, damped, adjustable compound pendulum for intermediate demonstrations and labs.
3A95.25stopped springAJP 51(7),655Complete discussion and analysis of a stopped spring system.
3A95.26non-linear springsAJP 32(2),xiiiTwo springs are attached in a "Y" arrangement, tie a string at two points along a spring so it becomes taut when extended, commercial "constant tension springs".
3A95.28rubber band oscillationsAJP 42(8),699A review of the foundations a of the rubber band force law and how it applies to the oscillations of a loaded rubber band.
3A95.31beyond SHMTPT 13(6),367Shadow project an inertial pendulum onto a selenium photocell and display the resulting voltage on an oscilloscope. Distortion at large amplitude is apparent.
3A95.32beyond SHMAJP 44(7),666The design of a pendulum that can demonstrate the dependence of period on amplitude. Common laboratory supplies are used for construction, and timing is done with a stopwatch. Agreement between experimental data and theory to 1 in 1000 is conveniently obtainable.
3A95.32large amplitude pendulumAJP 45(4),355Use a rod instead of a string to support the bob and angles can reach 160 degrees. Construction details are given.
3A95.33pendulum with large amplitudePIRA 1000
3A95.33pendulum with large amplitudeDisc 08-17Vary the from 5 to 80 degrees.
3A95.35non-harmonic air gliderAJP 40(5),779A Jolly balance spring is attached from a point above the middle of an air track to the top of a glider.
3A95.36nonlinear air track oscillatorAJP 50(3),220A length of rubber perpendicular to the air track axis provides a restoring force. Relative strengths of linear and nonlinear terms can be easily varied.
3A95.37saline nonlinear oscillatorAJP 59(2),137A small cup with a hole in the bottom and filled with salt water is placed in a large vessel of pure water. The system does all sorts of nonlinear stuff that can be reproduced by numerical simulation.
3A95.38perodic non-simple harmonic motionPIRA 1000
3A95.38periodic non-simple harmonic motionDisc 08-23A large pendulum drives a restricted vertical pendulum.
3A95.41anharmonic LRC circuitAJP 53(6),574A linear LRC circuit demonstrates "soft" and "hard" spring nonlinear resonant behavior.
3A95.43anharmonic oscillatorAJP 52(9),800An op amp with RC feedback network that behaves as a SHM oscillator for small inputs and then shifts to anharmonic when slew limiting occurs.
3A95.45amplitude jumpsPIRA 1000
3A95.45amplitude jumpsAJP 35(10),961Non linear oscillators driven by a variable periodic force: two systems are described.
3A95.46anharmonic air track oscillatorAJP 36(4),326A driven air cart between two springs has a magnet on top. Perturbations are introduced by other magnets. Jump effect is shown.
3A95.46amplitude jumpsAJP 38(6),773Use the small Cenco string vibrator to demonstrate amplitude jumps.
3A95.50chaos systemsPIRA 1000
3A95.50five chaos systemsAJP 55(12),1083Five simple systems, both mechanical and electronic, designed to demonstrate period doubling, subharmonics, noisy periodicity, and intermittent and continuous chaos.
3A95.51chaos in the bipolar motorAJP 58(1),58A simple bipolar model demonstrates chaos on the overhead projector. Plots require a digital scope or other equipment.
3A95.53mechanical chaos demonstrationsTPT 28(1),26Three mechanical chaos demonstrations: paperclip pendulum over two disk magnets, balls in a double potential well, ball rolling on a balanced beam.
3A95.54inverted pendulum chaosAJP 59(11),987A driven inverted pendulum goes through the transition from periodic to chaotic motion and a sonic sensor is used to get data to a computer which does a FFT to get the power spectrum.
3A95.55double scroll chaotic circuitAJP 58(10),936A simple electronic circuit shows double scroll chaotic behavior on an oscilloscope. A simple program to display computer simulation is also included.
3A95.55electronic chaos circuitAJP 53(4),332An electronic circuit implementing a coupled logistic equation is used to demonstrate chaotic behavior in one or two dimensions on an oscilloscope
3A95.60parametric resonancePIRA 1000
3A95.60parametric resonanceAJP 50(6),561A connecting-rod crank system to give vertical SHM to a pendulum. The parametric resonance state occurs when the pendulum is driven vertically at twice its frequency.
3A95.61parametric phenomenaAJP 39(12),1522Parametric excitation of a resonant system is self excitation caused by a periodic variation of some parameter of the system. A brief history.
3A95.62pendulum parametric amplifierAJP 28(5),506On using a self-oscillating pendulum driver to demonstrate parametric amplification.
3A95.63hula-hoop theoryAJP 28(2),104The hula-hoop as an example of heteroparametric excitation.
3A95.66magnetic dunking duckAJP 29(6),374Beak on a dunking duck is a magnet that triggers the driving circuit.
3A95.70pump a swingPIRA 1000
3A95.70pump a swing3A95.70Periodically pull on the string of a pendulum.
3A95.70pump a swing15-1.15A ball on a string hangs over a pulley. Increase the amplitude by pulling on the string periodically.
3A95.70pump a swingM-182Diagram. A electromagnet on a swing allows one to raise and lower the center of mass by a switch.
3A95.70pump a swingM-181Work up a swing by pulling on the cord at the right time.
3A95.70pump pendulumDisc 09-04Periodically pull on the string of a pendulum.
3A95.71more on pumping a swingAJP 38(7),920A pumped swing is analyzed and demonstrated as a simple pendulum whose length is a function of time.
3A95.71pumping a swing commentsAJP 37(8),843Also discuss as an example of parametric amplification. Demonstration of the amplification process is shown.
3A95.72pump a swingAJP 36(12),1165Analysis and a picture tracing out three and one half cycles.
3A95.73swingingAJP 44(10),924Parametric amplification and starting from rest.
3A95.73pump a swingAJP 38(3),378The point-mass model of AJP 36(12),1165 prohibits starting from rest. This simplified rigid body model is sufficient to demonstrate the start from rest.
3A95.73pump a swingAJP 39(3),347More on the first pump.
3A95.73start a swingAJP 40(5),764Now we use a rigid swing support instead of a rope.
3A95.80parametric instabilityPIRA 1000
3A95.80parametric instability3A95.80Same as AJP 48(3),218.
3A95.80parametric instabilityAJP 48(3),218Two springs in parallel support a block from which a "Y" pendulum swings. The two lowest order resonances are described in detail.

ReferenceDescription
M-1Sutton
Ma-1Freier & Anderson
M-1dHilton
8-2.8Meiners
1A12.01University of Minnesota Handbook
AJP 52(1),85American Journal of Physics
TPT 15(5),300The Physics Teacher
Disc 01-01The Video Encyclopedia of Physics Demonstrations

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