Table of Waves and Sound Waves and Sound(3B): Wave Motion Lecture Demonstrations

## Oscillations

PIRA classification 3A

Please note that these tables have not yet been edited to match the equipment that is available within the UW-Madison lecture demo lab. There maybe many items listed within these tables that we either "can not do" or have available.

# 3A10. Pendula

 PIRA # Demonstration Name Abstract 3A10.10 Simple_Pendulum Suspend a simple pendulum from a ringstand or hold by hand, and provide some energy allowing it to oscillate. 3A10.13 simple pendulum bobs An apparatus for open-ended investigation of the simple pendulum. Bobs have adjustable length and are of different shape. 3A10.14 4:1 pendulum 3A10.14 4:1 pendula 4:1 pendula have 2:1 period. 3A10.15 bowling ball pendulum 3A10.15 bowling ball pendulum Suspend a bowling ball from the ceiling. 3A10.17 different mass pendula 3A10.17 lead and cork pendula Long pendula made of lead and cork are released simultaneously. 3A10.17 different mass pendula Pendula of the same length and different mass oscillate together. 3A10.20 upside-down pendulum 3A10.20 upside-down pendulum A vertical leaf spring supported at the base has a movable mass. 3A10.20 inverted pendulum A piece of clockspring mounted vertically on a heavy base has an adjustable mass to change the period. 3A10.21 metronome as a pendulum The metronome as an adjustable pendulum. 3A10.30 Torsion_Pendulum Weight is added to a torsion pendulum to decrease the period of oscillations. 3A10.31 Torsion Pendulum A large clock spring oscillates an air bearing supported disc. Vary mass, damping, etc. 3A10.31 Torsion Pendulum A large clock spring oscillates a vertical rod with an adjustable crossbar. 3A10.32 Torsion Pendulum Calculate angular velocity and acceleration with a large slow torsion pendulum that has movable timer contacts. 3A10.34 crossed dumbell pendulum Crossed dumbbells with adjustable masses are mounted on an axle as spokes of a wheel. Show the dependence of the period on rotational inertia and on the distance between the center of gravity and axis of the pendulum. 3A10.35 torsion pendulum Strobe photography of a torsion pendulum. 3A10.40 variable g pendulum 3A10.40 variable g pendulum A pendulum with a bifilar support of solid rods can be inclined to decrease apparent g. 3A10.40 variable angle pendulum A physical pendulum is mounted on a bearing so the angle of the plane of oscillation can be changed. 3A10.42 variable g pendulum Use an electromagnet under the pendulum bob to increase the apparent g. 3A10.42 variable g pendulum A hidden electromagnet causes a variation in period of a iron pendulum bob. 3A10.44 variable g pendulum An evaluation of the model M110 Variable g Pendulum manufactured by Physics Apparatus Research Inc. Good pictures of the device for those interested in building their own. 3A10.50 cycloidal pendulum Demonstrate that a cycloidal pendulum with any amplitude has a period identical to a equal length simple pendulum at small amplitude. Construction details p. 603. 3A10.50 cycloidal pendulum A pendulum made to swing at large amplitude in the cusp of an inverted cycloid is compared to a simple pendulum. 3A10.55 nonisochronism of pendulum Two identical pendula, started with large and small amplitudes, have different periods. 3A10.61 sliding pendulum A block of dry ice is placed on a large parabolic mirror or bent sheet metal trough for other (i.e., cycloidal) curves.

# 3A15. Physical Pendula

 PIRA # Demonstration Name Abstract 3A15.10 physical pendulum Any distributed mass pendulum. 3A15.10 physical pendulum set A reconstruction of a nineteenth-century physical pendulum set of four shapes of equal length mounted from a common bar. 3A15.10 other symmetrical shaped pendula Twenty various physical pendula and are shown. 3A15.12 balancing man physical pendulum The balancing man usually used to show stable equilibrium is used here as a physical pendulum. 3A15.13 rocking stick A meter stick with small masses at the ends rocks on a large radius cylinder. Derivation. 3A15.20 oscillating bar 3A15.20 oscillation bar A bar is suspended from pivots at 1/6 and 1/4 of its length. A companion simple pendulum is used for comparison. 3A15.20 oscillating bar Analysis of the oscillating bar with a graph of typical data. 3A15.20 oscillating bar Analysis of the oscillating bar includes suspending the bar from a string. 3A15.20 oscillating bar Suspend the meter stick from one end and find the center of oscillation with a simple pendulum of the same period. 3A15.20 physical pendulum Compare the period of a bar supported at the end with a simple pendulum of 2/3 length. 3A15.21 two rods and a ball A rod pivots at a point 2/3 l, a second rod 2/3 l pivots at the end, and a simple pendulum has length 2/3 l. Then pivot the long rod from the end and compare periods. 3A15.25 oscillating hoop 3A15.25 oscillating hoop A hoop and pendulum oscillate from the same point. 3A15.25 oscillating hoop Adjust a simple pendulum to give the same period as a hoop. 3A15.30 paddle oscillator 3A15.30 paddle A physical pendulum that oscillates with the same frequency from any of a series of holes. 3A15.30 paddle An odd shaped object oscillates from conjugate points that give the physical pendulum equal periods. 3A15.31 triangle oscillator Suspend a meter stick four different ways with the same period of oscillation. Holes are drilled on two concentric circles about the center of mass of a large triangle such that the period of oscillation is always the same. 3A15.35 bent wire Measure the period of a two corks on a bent wire physical pendulum with the wire bent to various angles. 3A15.40 truncated ring 3A15.40 truncated ring Same as AJP 35(10),971. 3A15.40 truncated ring Removing any part of the hoop will not change the period. 3A15.40 hoops and arcs A hoop oscillates with the same period as arcs corresponding to parts of the hoop. 3A15.45 oscillating lamina 3A15.45 oscillating lamina Same as TPT 4(2), 78. But where is the reference? 3A15.50 sweet spot 3A15.50 sweet spot A baseball bat on a frame is rigged to show the motion of the handle end when the bat is hit on and off the center of percussion. 3A15.50 center of percussion Hang a rod from a thin steel rod that acts as both a support and a pivot. A styrofoam ball on the thin rod is an indicator of the motion of the end of the hanging rod. 3A15.50 sweet spot Hit a baseball bat on a rail suspension at points on and off the center of percussion. 3A15.50 center of percussion Hang a long metal bar by a string from one end. Strike the bar with a mallet at various points. 3A15.52 sweet spot Fire a spring powered gun at a meter stick loosely supported on one end. The top jumps one way or the other when hit off the center of percussion. 3A15.53 sweet spot Strike a meter stick supported by a matchstick at its center of percussion. Repeat off the center of percussion and break the matchstick. May be scaled up. 3A15.54 sweet spot A bunch of corks sit on a meter stick on the lecture bench. Hit the stick near the end and as it moves down the table the cork at the center of percussion will remain on the stick. 3A15.55 sweet spot A rectangular bar suspended by a thread along with an adjustable simple pendulum. Strike the bar. 3A15.55 sweet spot Strike a heavy metal bar suspended by a string at various points. 3A15.56 sweet spot A rectangular bar is supported as a physical pendulum from one of two pivots along with a simple pendulum. 3A15.57 sweet spot of a meter stick 3A15.57 sweet spot of a meter stick 3A15.58 sweet spot A bat is suspended from a horizontal cable under tension. When struck off the center of percussion, vibrations in the cable cause a neon lamp to light. 3A15.59 sweet spot analysis The different definitions of the term "sweet spot" are discussed, each one based on a different physical phenomenon. 3A15.59 analysis of the sweet spot Analysis of the three sweet spots of the baseball bat and the location of the impact point that gives maximum power. 3A15.70 Kater's pendulum 3A15.70 Kater's pendulum Modification of a Welch Kater pendulum so that it may be used more systematically and with improved precision to measure the acceleration due to gravity. 3A15.70 Kater's pendulum An elaborate pendulum that allows "g" to be determined accurately. 3A15.72 Kater's pendulum Analysis of: if the center of mass is halfway between the pivots, g cannot be determined from measurements of equal period alone.

# 3A20. Springs and Oscillators

 PIRA # Demonstration Name Abstract 3A20.10 mass on a spring A mass oscillates slowly on a large spring. 3A20.10 mass on a spring A kg and other masses oscillate on a spring with a constant of about 30 N/m. 3A20.10 mass on a spring Mass on a spring. 3A20.10 mass on spring Double the mass on the same spring. Try identical springs in parallel. 3A20.11 bouncing students Students are bounced from GM car hood springs. Examine the period with different students on board. 3A20.12 mass on a spring A shortcut method for constructing a vertical spring oscillator of predetermined period. 3A20.13 mass on a spring Use a slinky for a spring and vary k by using different numbers of turns. 3A20.16 mass on a spring A discussion of the complexities of the vertical mass on the spring in comparison to the horizontal case. 3A20.20 springs in series and parallel 3A20.20 springs in series and parallel Hang a mass from a spring, 1/2 mass from two springs in series, and 2m from springs in parallel. 3A20.30 air track glider and spring An air cart is attached to a single horizontal coil spring. 3A20.30 air track glider and spring An air cart is attached to a single horizontal coil spring. 3A20.30 air track glider and spring Horizontal mass and single spring on the air track. 3A20.31 air track glider and spring Four methods of determining Hooke's law with a air cart and spring. 3A20.35 air track glider between springs 3A20.35 air track glider between springs 3A20.35 air track mass between springs A mass between two springs on an air track. 3A20.35 air track simple harmonic motion Place an air track glider between two springs. A video overlay overlay shows the sinusoidal path. 3A20.36 dry ice puck oscillator A dry ice puck between two springs on a plate of glass. Projection, photocell velocity measurement, etc. 3A20.40 roller cart and spring 3A20.40 roller cart and spring Attach a large horizontal compression spring to a large heavy roller cart. 3A20.50 oscillating chain 3A20.50 oscillating chain Tie the ends of a short logging chain with heavy thread and suspend the thread over a pulley. 3A20.50 oscillating chain A chain suspended on both ends by a string which runs over a pulley. 3A20.50 oscillating chain Ends of a chain are connected with string and hung over a large pulley. 3A20.55 "U" tube An open "u" tube filled with mercury. 3A20.60 ball in spherical dish A ball oscillates in a clear spherical dish on the overhead. 3A20.65 differences in harmonic motion A plastic hemisphere rocking in water has a higher frequency than when rocking on a level surface. 3A20.70 diatomic molecule oscillator Two dry ice pucks coupled with vertical hacksaw blades attached to a steel bar. 3A20.90 simple non-harmonic motion A light car is fastened between two springs and then between two pulleys with hanging weights. In the the second case the period in dependent on amplitude.

# 3A40. Simple Harmonic Motion

 PIRA # Demonstration Name Abstract 3A40.10 circular motion vs. mass on a aspring Shadow project a ball at the edge of a disc rotating at the same frequency as a mass on a spring. 3A40.10 projected SHM A rotating disc with a ball and a mass on a spring are shadow projected on the wall. 3A40.10 circular motion vs. spring and weigh Front on view of a marker on a disc and a mass on a spring. 3A40.12 circular motion vs.pendulum/spring A bike wheel with a ball mounted on the rim can be oriented with the axle vertical when shadow projected with a pendulum or with the axis horizontal when shadow projected with a mass on a spring. 3A40.15 pendulum vs. mass on spring A dry ice puck between two horizontal springs oscillates under a long pendulum. 3A40.18 Rotating_Gizmo A device operated with a hand crank causes two small, circular discs to move in simple harmonic motion. One disc moves in a circular path while the other moves in a vertical line showing the physical correspondence of SHM with the "unit" circle (sinusoidal functions). 3A40.20 circular motion vs. pendulum Shadow project a pendulum and turntable which have identical frequencies. 3A40.20 circular motion vs. pendulum Shadow project a pendulum and a turntable with a ball mounted on the rim. 3A40.20 pendulum SHM Shadow project a pendulum and turntable which have identical frequencies. 3A40.20 pendulum SHM Using a 78 rpm phonograph turntable to synchronize a pendulum and ball on a turntable. 3A40.20 pendulum SHM A pendulum bob and shadow projection of circular motion of the same frequency appear coupled. 3A40.20 circular motion vs. pendulum Front view of a marker on a disc and a pendulum. 3A40.21 pendulum SHM A pendulum bob is shadow projected along with a post rotating on a turntable. 3A40.22 Ball on "U" Tracks A ball is rolled on a symmetric "U" shaped track to show harmonic motion and compared to a symmetric elongated "U" shape track to show non-harmonic motion. 3A40.25 ball on track vs. pendulum 3A40.27 portulum In a variation of the simple swinging pendulum, the "portulum", a ball, driven by short blasts of air, rolls along a curved tube. The oscillations of the rolling ball have the same mathematical form as the oscillations of a ball swinging along the same path, but with a lower frequency. 3A40.30 arrow on the wheel 3A40.30 arrow on the wheel An arrow that can be oriented tangentially or radially is mounted at the edge of a rotating disc and shadow projected on the wall. 3A40.30 arrow on mounted wheel A large arrow that can be oriented either tangentially or radially is mounted on the periphery of a rotating disc and shadow projected on a screen. 3A40.30 mounted wheel An arrow at the edge of a rotating disc that can be oriented radially or tangentially is shadow projected onto a wall. 3A40.31 arrow on the wheel Shadow project a crank handle oriented perpendicular to the wall or screen. 3A40.32 SHM vectors Three arrows are soldered on a rotating spindle: acceleration, velocity, and displacement vectors. The device is shadow projected on a screen. 3A40.35 SHM slide 3A40.35 SHM slide A motorized device inserted in a lantern slide projector shows a rotating spot and a SHM spot. 3A40.35 SHM slide A motorized lantern slide showing both rectilinear SHM and uniform circular motion. 3A40.35 SHM Slide A projection slide device that shows one spot moving in circular motion and another in SHM. 3A40.36 SHM slide Use a scotch cross mechanism (drawing) and mount colored discs on the circular pin and SHM pin. 3A40.38 SHM on CRO Using electronics and three oscilloscopes to show a spot moving in a circle, up and down with SHM, and a sine wave. A method for doing this sequentially on only one oscilloscope is also given. 3A40.40 project SHM Project a beam of light off a mirror on a tuning fork to a rotating mirror onto a screen. 3A40.41 tuning fork with light 3A40.41 tuning fork with light Attach a small light to a large slow fork and pan it by a video camera. A sine wave is visible by camera retention. 3A40.45 pendulum interface - Apple II An induced EMF from the magnet bob and an ADC forms the basis for this interface. 3A40.45 displaying pendulum motion The free end of the pendulum carries a pin electrode in a water trough with electrodes at each end. The signal is displayed on a oscilloscope. 3A40.48 plotting SHM A bifilar pendulum with a marker traces on a sheet of wrapping paper advanced by a motor. 3A40.50 strain gauge SHM 3A40.50 strain gauge SHM A spring and mass are suspended from a Pasco dynamic force transducer and the force is displayed on an oscilloscope. 3A40.50 strain gauge SHM Mass on spring hangs from a Pasco strain gauge with the output to a oscilloscope. 3A40.52 mass-spring on scope An optoelectronic device to display the displacement of a mass-spring system on the oscilloscope. 3A40.53 mass-spring accelerometor A "U" tube manometer is placed on a cart between springs to show acceleration in SHM. 3A40.60 acceleration in a pendulum Use the Project Physics accelerometer as a pendulum with a ballistic pendulum suspension. 3A40.65 phase shift disc 3A40.65 phase shift Shadow project two balls mounted on the edge of a disc. Vary the angle between the balls to vary the phase shift. 3A40.71 plotting SHM on the OH An acetate roll is motorized on the OH projector. Another motor drives a pen in SHM. 3A40.72 plotting SHM with spray paint A can of spray paint oscillating between two springs traces on a roll of paper towels pulled uniformly by the instructor. 3A40.75 plotting SHM A large ball oscillates on a spring and a pen on a rider below the ball traces on a roll of moving paper. 3A40.80 analysis,etc A collection of 16 physical systems which oscillate with SHM and one that does not. Analyses are given for several. 3A40.81 plate on drums A plate resting on two oppositely rotating drums (wheels) exhibits SHM. Includes Derivation. 3A40.82 "Atwood's" oscillator An advanced SHM system of a weight hanging from the edge of a solid disk weighted with an additional off center mass. 3A40.90 photographing SHM How to photograph a mass on a spring using a camera and a strobe. Also a hint about using a slit in a cardboard mask in front of an oscilloscope with a sine wave. 3A40.91 photographing SHM Take strobe wheel photographs of a pendulum light and a mass on a spring light. 3A40.93 photographing SHM Photograph a blinky that translates and oscillates.

# 3A50. Damped Oscillators

 PIRA # Demonstration Name Abstract 3A50.10 dash pot A mass on a spring has a paddle that can be placed in water for damping. 3A50.10 dash pot A mass on a spring has an attached dash pot for critical damping. 3A50.10 dash pot Three identical masses on springs with different size vanes in water provide under, over, and critically damped oscillations. 3A50.20 damped SHM tracer 3A50.20 damped SHM tracer A mass on a spring holds a magic marker that traces on paper the instructor pulls off a roll. 3A50.40 double spring damped air cart A long spring is attached to each end of the air track. Magnets are used for damping. 3A50.42 small air track oscillator A small specially constructed air track and optoelectric transducer provide output of position vs. time. Details of circuit and description of air track construction are included. 3A50.45 oscillating guillotine 3A50.45 oscillating guillotine Sets of magnets provide variable damping of an oscillating aluminum sheet. 3A50.50 bouncing magnets Magnets are levitated on a rod. A large area photocell is used to detect the position of the levitated magnet as it oscillates. 3A50.60 tuning fork Display tuning fork vibrations on an oscilloscope. Modeling clay between the forks increases damping. 3A50.65 steel bar Apparatus to displace a small steel bar and pick up the vibrations electromagnetically for display on an oscilloscope. 3A50.70 ship stabilizer A rocking closed circuit "U" tube half filled with colored water has a rubber hose and tube clamp for adjusting the damping. Demonstrates a ship stabilizing system 3A50.75 water balloon oscillator Two balloons full of water are mounted on the ends of a glass tube. Flatten one balloon and the system will oscillate about six times. 3A50.90 analog computer simulation Simulating an automobile suspension system with an analog computer.

# 3A60. Driven Mechanical Resonance

 PIRA # Demonstration Name Abstract 3A60.10 The film loop lasts 7min. A film of the collapse of the bridge due to resonance and how it was built. 3A60.11 Tacoma Narrows On building a model of the Tacoma Narrows bridge. 3A60.12 engineering analysis of the bridge Understanding gained from full, dynamically scaled models of the bridge is fundamentally different form the explanation in most physics texts. 3A60.20 driven glider on air track 3A60.20 driven glider on air track A cart is placed between two long springs driven by a variable speed motor. 3A60.20 driven glider on air track Drive an air glider between two springs. 3A60.24 driven cart between springs A PSSC cart is driven by a ratio motor between two springs. Use eddy current damping. 3A60.24 driven cart between springs A more complex driven cart between two springs with eddy current damping and recording. Construction details p. 549. 3A60.24 driven cart between springs A cart between stretched rubber bands is driven by an eccentric on a variable speed motor. Eddy Current damping. 3A60.25 driven glider on air track A driven air track cart has an adjustable vane in a tank of water. Graphs of amplitude with varying damping are generated the old fashioned way. 3A60.30 Barton's pendula 3A60.30 Barton's pendula A set of pendula of increasing length are driven in common at varying frequencies. 3A60.30 Barton's pendula A simple implementation of Barton's pendula. 3A60.30 Barton's pendula Several pendula of graduated length are hung from the same driven support. 3A60.30 Barton's pendula Many of different length small pendula are hung from a rod driven by an adjustable heavy pendulum. 3A60.31 resonant driven pendula 3A60.31 resonant driven pendula A massive pendulum drives three different length bifilar pendula. 3A60.35 bowling ball pendulum resonance 3A60.35 torsion resonance Driving a torsion pendulum with a jigsaw. 3A60.35 torsion resonance An air bearing supported disc/large clock spring arrangement is variably driven. Also vary damping, mass. 3A60.35 bowling ball pendulum resonance Strike a bowling ball pendulum with random blows, then with blows at the normal frequency. 3A60.36 impulse driven torsional oscillator Apparatus Drawings Project No. 23: Plans for a simple impulse driven torsion pendulum with a natural period of 2 sec. 3A60.37 driven torsional oscillator Upper and lower discs are connected by an axial wire. The upper is driven in SHM and the resulting motion of the lower is studied. 3A60.39 Driven Mass on a Spring A function generator drives a spring with a suspended mass. The frequency is adjusted until resonance is reached. 3A60.40 Driven Harmonic Motion Analyzer A Pasco apparatus is used to drive a vertical mass on a spring to show phase differences above and below resonance. 3A60.41 mechanical analog of electrical res. A driven system of a mass hanging between two springs. 3A60.42 driven resonance tracer A driven mass between two springs carries a felt tip marker that traces on graph paper pulled at a steady rate. 3A60.43 driven spring weight 3A60.43 driven spring weight Drive a mass hanging from a spring. 3A60.44 drunken sailor 3A60.44 drunken sailor A hollow toy "Donald Duck" is driven between two vertical springs. Enough "wine" is poured in to reach resonance and then enough "coffee" is poured in to overshoot resonance. 3A60.44 drunken sailor A bottle (sailor) between two springs is driven at resonance when half full of water. Start empty, add wine to half full, fill with coffee to sober him up. 3A60.45 hand driven rubber tube Longitudinal oscillations are induced by hand on a long rubber tube with a wood block attached in the middle. 3A60.46 spring driven spring on a spring A large spring and adjustable mass on a lever arm drives a small mass on a spring with provisions for damping. 3A60.47 driven mass on spring Apparatus Drawings Project No.8: A vertical mass on a spring with a variable frequency driver and adjustable damping. 3A60.48 driven mass spring apparatus Optical transmission wedges are used to measure positions of both sides of the spring. 3A60.48 electromagnetically driven apparatus A magnet hanging on a spring oscillates in a tube with several windings, one serves as a pickup to an oscilloscope, another as a driver, others as means of introducing damping forces. 3A60.48 electromechanical shaker/accelerometer A small accelerometer is placed on a mass driven by a commercial electromagnetic shaker. 3A60.50 resonance reeds 3A60.50 resonance reeds 3A60.50 resonance reeds A set of steel reeds is mounted on a common excited strip. 3A60.50 resonance reeds A large scale resonance reed set is driven by a motor. 3A60.50 resonance reeds A set of resonance reeds is mounted on a slightly unbalanced gyrowheel. 3A60.50 resonance reeds A set of resonance reeds is mounted on a out of balance gyroscope. 3A60.50 reed tachometer A set of reeds is attached to a small unbalanced gyro. 3A60.51 resonance reeds A steel bar has pairs of inverted pendula attached along its length. Vibrating a particular rod will cause its mate to vibrate but not the others of different length. 3A60.53 resonance reeds A vacuum cleaner motor with an eccentric mass is clamped to a long steel strip hanging over the edge of the lecture bench. 3A60.55 driven torsion pendulum 3A60.56 galvanometer movement resonance A galvanometer movement (observed by reflected laser beam) driven by a slow function generator (observed on an oscilloscope) shows both driving and driven motions. 3A60.56 galvanometer movement oscillations Record the motion of the galvanometer movement by modulating the radial magnetic field at a frequency beyond the response of the movement and detecting the induced current. 3A60.57 galvanometer movement oscillations Drive a wall mount galvanometer (period 20 sec.) with a low frequency signal generator. 3A60.58 water dropper resonance The frequency of drops striking a bar clamped at one end is adjusted so that they match the natural frequency of a bar. 3A60.60 upside-down pendulum 3A60.60 upside-down pendulum Same as Mz-9. 3A60.60 upside-down pendulum A variable speed motor provides vertical undulatory motion for a vertical rod with an adjustable mass. 3A60.61 inverted pendulum - portable jigsaw Strobe pictures along with some theory of an inverted pendulum driven with a portable jigsaw. 3A60.61 inverted pendulum - saber saw Mount a short stick on the blade of an inverted saber saw. 3A60.62 inverted pendulum - liquid Demonstration and theory of an inverted liquid pendulum. 3A60.63 inverted pendulum - an analog The inverted pendulum is presented as an analog of the quadrupole mass filter. Theory of the inverted pendulum is discussed. 3A60.64 inverted pendulum - speaker driven The inverted pendulum is analyzed using a series of short impulses instead of sinusoidal excitation. A large loudspeaker with a 3/4" movement is used to drive simple and compound inverted pendula. 3A60.67 upside-down pendulum A massive (20 lb.) weight is bolted to an upright leaf spring from an auto and exited by a thread. 3A60.70 lamppost resonance 3A60.70 lam post resonance A three meter steel rod model of a lam post weighted at the top is easily resonated by hand until a bolt in the support platform breaks. 3A60.75 driven conical pendulum A variable length conical pendulum is driven at a single frequency and the phase is compared to a reference. 3A60.80 Calthrop resonance pendulum Drive a heavy compound pendulum which in turn drives a light simple pendulum. 3A60.81 Rayleigh's dirven pendulum Lord Rayleigh's method of suspending a light pendulum from a heavy driving pendulum. 3A60.85 pendulum in a dish ???? This is a model of aeolian sounds. Read it yourself. 3A60.89 paddleball - non SHM A paddleball is a non-SHM system that can be used to demonstrate resonance. 3A60.90 mechanical vibrator A SHM driver can be made from a old truck flywheel on bearings attached to a crank. 3A60.91 mechanical vibrator Commercial motor driven mechanical vibrators are available. 3A60.92 mechanical vibrator A heavy pendulum on a knife edge can be used to generate horizontal motion of periods from 1 to 10 seconds. 3A60.93 mechanical vibrator A vibrator of fixed period is made from a clock motor. 3A60.94 Macalaster-PSSC oscillator An apparatus for many demonstrations in mechanical resonance.

# 3A70. Coupled Oscillators

 PIRA # Demonstration Name Abstract 3A70.10 Wilberforce pendulum Energy transfers between vertical and torsional modes. 3A70.10 Wilberforce pendulum A mass on a spring with outriggers is tuned so the three modes of oscillation will couple. 3A70.10 Wilberforce pendulum The Wilberforce pendulum. 3A70.10 Wilberforce pendulum Transfer of energy between torsional vibration and vertical oscillation in the Wilberforce pendulum. 3A70.10 Wilberforce pendulum Shows two Wilberforce pendula. 3A70.10 Wilberforce pendulum A small Wilberforce pendula. 3A70.10 Wilberforce pendulum Energy transfers between vertical and torsional modes. 3A70.11 Wilberforce pendulum analysis Analysis of the Wilberforce pendulum. Compare theory with experiment. 3A70.12 Wilberforce pendulum Directions for making an inexpensive Wilberforce pendulum, including winding the spring. 3A70.14 swinging mass on a spring Derivation with the additional hint that you can use a weak spring by adding a length of string to increase the period of the pendulum motion. 3A70.15 swinging mass on a spring 3A70.15 swinging mass on a spring The oscillation mode of a mass on a spring couples with the pendulum mode. 3A70.15 swinging mass on a spring Analysis of autoparametric resonance that occurs when the rest length of a spring is stretched by about one third by a mass. 3A70.15 swinging mass on a spring Oscillations couple if the frequency of a mass on a spring is twice the pendulum mode frequency. 3A70.16 swinging mass on a spring -uncoupled The special case in which the angular frequency of the spring and the frequency of the pendulum are equal, where the equations of motion actually uncouple and yield independent vertical and pendular motion. The simple apparatus is shown. 3A70.17 spring pendulum Time the period of a 12" pendulum, take a 12" spring and add mass until the period is the same. Show the extension is 12" 3A70.20 coupled pendula Hang two or three pendula from a flexible metal frame. 3A70.20 coupled pendula Two pendula are hung from a flexible metal frame. A third can be added. 3A70.20 coupled pendula Two bobs suspended from a suspended horizontal dowel. 3A70.20 coupled pendula Rods and spring steel support two pendula. The picture is less than clear. 3A70.21 coupled pendula There identical pendula are coupled by a slightly flexible support. 3A70.21 coupled pendula Three identical pendula hang from a slightly flexible stand. 3A70.22 projection coupled pendula Two small coupled pendula hang from a slightly flexible stand on a clear base. 3A70.25 spring coupled pendula 3A70.25 spring coupled pendula Two pendula are coupled with a light spring. 3A70.25 spring coupled pendula Two equal adjustable pendula coupled with a light spring. 3A70.26 spring coupled pendula Two identical bobs are coupled with a leaf spring. 3A70.27 spring coupled physical pendula 3A70.27 coupled pendula Two bowling ball bobs on aluminum rods allowing for length adjustments are coupled with a light spring between the rods. 3A70.27 coupled pendula Two physical pendula are coupled by a spring. 3A70.30 string coupled pendula 3A70.30 string coupled pendula Pendula are suspended from a horizontal string. 3A70.30 string coupled pendula Theory and diagram of the string-coupled pendula. 3A70.30 string coupled pendula Two pendula are coupled on a string. Coupling time depends on the string tightness, amplitude depends on the mass. 3A70.30 string coupled pendula Two pendula are suspended from a common string. 3A70.31 triple pendula A spring coupled triple pendulum used to demonstrate the character of normal modes and in particular a mode that has high Q even with the center pendulum highly damped. The mathematically similar to the equations of three coupled quantum mechanical levels. 3A70.32 resonant double pendulum This double pendulum system with modes that differ by a factor of two has not yet been completely solved. 3A70.33 varied length coupled pendula A symmetrical arrangement of seven steel balls are coupled 6" below their anchor points with a long wooden bar through which the cords pass. Energy transfers from one end to the other. 3A70.35 double simple pendulum Analysis of two masses on the same string with combination of the masses and strings being equal or unequal. 3A70.36 over-under pendula A light pendulum suspended from a heavy pendulum. 3A70.38 electrostatically coupled pendula Two pith ball pendula couple only when they are charged with the same polarity. 3A70.40 inverted coupled pendula 3A70.40 inverted coupled pendula Two vertical hacksaw blades with weights at the top are coupled at the bottom. 3A70.41 coupled upside down pendula Two adjustable upside down pendula are coupled with a rubber band. Also shows beats. 3A70.45 coupled masses on springs 3A70.50 oscillating magnets 3A70.50 oscillating magnets You really have to see the picture of this to believe it. 3A70.55 coupled compass needles Oscillations of two compass needles couple. 3A70.56 coupled magnets Two magnets are suspended from a suspended wooden wand, all horizontal. Oscillations couple and attain a final north-south alignment. 3A70.60 ball & curved track pendulum Analysis of the peculiar motion of a quarter circle track pendulum with a ball bearing. 3A70.70 rotating 2D coupled oscillations Examine the oscillations of a "Y" pendulum as it is rotated at varying speeds.

# 3A75. Normal Modes

 PIRA # Demonstration Name Abstract 3A75.10 coupled harmonic oscillators Many identical air track gliders are coupled with springs and driven with a variable frequency motor. 3A75.10 coupled harmonic oscillators Article on identical spring coupled air gliders includes theory. 3A75.10 coupled harmonic oscillators Several identical air track gliders are coupled with identical springs. 3A75.10 coupled harmonic oscillators A driven chain of air gliders and springs. Big write up. 3A75.11 coupled harmonic oscillators Five blocks coupled with coil springs ride in an air trough. 3A75.12 coupled harmonic oscillators A six meter chain of air supported pucks connected by a slinky. 3A75.12 coupled harmonic oscillators Six meters of dry ice pucks on a driven slinky. 3A75.30 masses on a string 3A75.30 masses on a string Clamp 1,2,3, or 4 equal masses to a variably driven wire to show normal modes. 3A75.31 weighted string Small lead weights on a string driven by a large motor show the lower normal modes of a many body system. 3A75.40 bifilar pendulum modes 3A75.40 bifilar pendulum All three modes of oscillation are discussed for horizontal rods supported with bifilar suspensions. 3A75.40 bifilar pendulum Discusses two of three modes - transverse in the plane of the cords and twisting. 3A75.45 selsyn motor pendula Pendula are hung from the shafts of two selsyn motors. The second mode can be demonstrated. 3A75.50 double pendulum Normal modes of a two pendula spring coupled driven system. 3A75.80 exposing normal modes When two modes are simultaneously exited, strobing the system at the frequency of one normal mode will allow the other to be observed independently. A double hacksaw system is used as an example.

# 3A80. Lissajous Figures

 PIRA # Demonstration Name Abstract 3A80.10 Lissajous sand pendulum A sand filled compound pendulum traces out a Lissajous pattern. 3A80.10 sand track Lissajous figures A compound pendulum drops sand out of the pendulum bob in a Lissajous pattern. 3A80.10 Lissajous sand pendulum A simple sand pendulum made by passing a bifilar suspension through an adjustable collar. 3A80.11 Lissajous figures in sand A compound pendulum bob traces a Lissajous figure in sand. 3A80.13 Blackburn pendulum A historical note on Blackburn's role in the "Y suspended" pendulum. ref: AJP 49,452-4 3A80.15 double pendulum "art machine" Design for a double pendulum machine that draws with a pen. 3A80.15 Lissajous figures - double pendulum Two adjustable physical pendula at right angles coupled to a pen. Diagram. 3A80.20 Lissajous figures - scope 3A80.20 Lissajous figures - scope Two generators are fed into the x and y channels of a scope. 3A80.20 Lissajous figures on the scope Two oscillators generate Lissajous figures of the X and Y channels on an oscilloscope. 3A80.20 Lissajous figures - scope Use two independent generators to show Lissajous figures on a scope. 3A80.21 Lissajous figures Lissajous figures on a scope and three other methods in a reprint. 3A80.22 Lissajous figures - scope Two sine waves are produced by coupling a variable speed motor to one pot in each of two Wheatstone bridge circuits. 3A80.30 Lissajous bar An oscillating one meter long bar with the width to length ratio a small integer will show a Lissajous pattern when clamped at one end and viewed from the other. 3A80.35 Lissajous figure vibrations A rectangular cross section rod is mounted vertically and the top is bent over at right angles. When the protruding end is struck it will describe Lissajous patterns. 3A80.40 Lissajous figures - laser 3A80.40 Lissajous figures - projected Use small mirrors on tuning forks to project a beam of light on the wall. 3A80.41 Lissajous figures - projected Bounce a laser off a soap film excited by a audio speaker and a Lissajous figure can be projected onto a screen. 3A80.43 Lissajous figures - harmonograph An elaborate apparatus made to reflect beams off mirrors - two oscillations in SHM and one that is the combination. 3A80.44 Lissajous figures - projected A sine wave of an integral number of periods is drawn on a clear cylinder. When projected on an overhead, any phase may be obtained by turning the cylinder 3A80.46 Lissajous figures - mechanical Chains, gears, etc., that allow control of amplitude, initial phase, and frequency of the two component vibrations. 3A80.50 Lissajous figures - 3d An elaborate setup that uses three motors to produce a spot of light on a card that is the result of three mutually perpendicular SHM's. 3A80.51 Lissajous figures - 3d A slit in a lantern projector is driven in SHM and the resulting light beam is projected onto a white pencil mounted on a disc rotated by a motor in the perpendicular direction. 3A80.60 textbook corrections Most Lissajous figures illustrated in textbooks are wrong. 3A80.90 characteristic triangle method A Lissajous ellipse is drawn using the characteristic triangle method. Fully derived instructions. 3A80.91 Lissajous coordinate system A coordinate system with the grid proportional to the sines of 0, 30, 60, and 90 degrees is sketched on the board.

# 3A95. Non-Linear Systems

 PIRA # Demonstration Name Abstract 3A95.10 water relaxation oscillator A cylinder is filled with water at a constant rate and periodically empties. 3A95.12 electrical and water relaxation osc. A water relaxation oscillator models a neon flasher relaxation oscillator. 3A95.13 pipet rinser oscillator The commercial pipet rinser is a much better relaxation oscillator than that in AJP 39(5),575. 3A95.15 wood relaxation oscillator A wood block rides up and slides back on the inside of a turning hoop. 3A95.20 wood block relaxation oscillator 3A95.20 water feedback oscillator A tubing and bellows arrangement to generate oscillations by feedback. Picture. 3A95.22 compound pendulum A driven, damped, adjustable compound pendulum for intermediate demonstrations and labs. 3A95.25 stopped spring Complete discussion and analysis of a stopped spring system. 3A95.26 non-linear springs Two 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". 3A95.28 rubber band oscillations A review of the foundations a of the rubber band force law and how it applies to the oscillations of a loaded rubber band. 3A95.31 beyond SHM Shadow project an inertial pendulum onto a selenium photocell and display the resulting voltage on an oscilloscope. Distortion at large amplitude is apparent. 3A95.32 beyond SHM The 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. 3A95.32 large amplitude pendulum Use a rod instead of a string to support the bob and angles can reach 160 degrees. Construction details are given. 3A95.33 pendulum with large amplitude 3A95.33 pendulum with large amplitude Vary the from 5 to 80 degrees. 3A95.35 non-harmonic air glider A Jolly balance spring is attached from a point above the middle of an air track to the top of a glider. 3A95.36 nonlinear air track oscillator A length of rubber perpendicular to the air track axis provides a restoring force. Relative strengths of linear and nonlinear terms can be easily varied. 3A95.37 saline nonlinear oscillator A 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. 3A95.38 periodic non-simple harmonic motion 3A95.38 periodic non-simple harmonic motion A large pendulum drives a restricted vertical pendulum. 3A95.40 Anharmonic_Ping_Pong_Ball A ping pong ball is dropped and then bounces anharmonically. 3A95.41 Anharmonic_Plate A heavy plate spinning on its side begins to fall in a circular fashion oscillating anharmonically until it comes to rest. 3A95.42 Anharmonic LRC Circuit A linear LRC circuit demonstrates "soft" and "hard" spring nonlinear resonant behavior. 3A95.43 Anharmonic oscillator An op amp with RC feedback network that behaves as a SHM oscillator for small inputs and then shifts to anharmonic when slew limiting occurs. 3A95.45 amplitude jumps 3A95.45 amplitude jumps Non linear oscillators driven by a variable periodic force: two systems are described. 3A95.46 anharmonic air track oscillator A driven air cart between two springs has a magnet on top. Perturbations are introduced by other magnets. Jump effect is shown. 3A95.46 amplitude jumps Use the small Cenco string vibrator to demonstrate amplitude jumps. 3A95.50 chaos systems 3A95.50 five chaos systems Five simple systems, both mechanical and electronic, designed to demonstrate period doubling, subharmonics, noisy periodicity, and intermittent and continuous chaos. 3A95.51 chaos in the bipolar motor A simple bipolar model demonstrates chaos on the overhead projector. Plots require a digital scope or other equipment. 3A95.53 mechanical chaos demonstrations Three mechanical chaos demonstrations: paperclip pendulum over two disk magnets, balls in a double potential well, ball rolling on a balanced beam. 3A95.54 inverted pendulum chaos A 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. 3A95.55 double scroll chaotic circuit A simple electronic circuit shows double scroll chaotic behavior on an oscilloscope. A simple program to display computer simulation is also included. 3A95.55 electronic chaos circuit An electronic circuit implementing a coupled logistic equation is used to demonstrate chaotic behavior in one or two dimensions on an oscilloscope 3A95.60 parametric resonance 3A95.60 parametric resonance A 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. 3A95.61 parametric phenomena Parametric excitation of a resonant system is self excitation caused by a periodic variation of some parameter of the system. A brief history. 3A95.62 pendulum parametric amplifier On using a self-oscillating pendulum driver to demonstrate parametric amplification. 3A95.63 hula-hoop theory The hula-hoop as an example of heteroparametric excitation. 3A95.66 magnetic dunking duck Beak on a dunking duck is a magnet that triggers the driving circuit. 3A95.70 pump a swing 3A95.70 pump a swing Periodically pull on the string of a pendulum. 3A95.70 pump a swing A ball on a string hangs over a pulley. Increase the amplitude by pulling on the string periodically. 3A95.70 pump a swing Diagram. A electromagnet on a swing allows one to raise and lower the center of mass by a switch. 3A95.70 pump a swing Work up a swing by pulling on the cord at the right time. 3A95.70 pump pendulum Periodically pull on the string of a pendulum. 3A95.71 more on pumping a swing A pumped swing is analyzed and demonstrated as a simple pendulum whose length is a function of time. 3A95.71 pumping a swing comments Also discuss as an example of parametric amplification. Demonstration of the amplification process is shown. 3A95.72 pump a swing Analysis and a picture tracing out three and one half cycles. 3A95.73 swinging Parametric amplification and starting from rest. 3A95.73 pump a swing The 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. 3A95.73 pump a swing More on the first pump. 3A95.73 start a swing Now we use a rigid swing support instead of a rope. 3A95.80 parametric instability 3A95.80 parametric instability Same as AJP 48(3),218. 3A95.80 parametric instability Two springs in parallel support a block from which a "Y" pendulum swings. The two lowest order resonances are described in detail.