#  Coupled Oscillations and Resonance 

 



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### Coupled Oscillators

\[S/M | t | —\]  
Long pendulums coupled by spring; also a pair of hacksaw blades magnetically coupled.  
  
\[[In-Depth Description](/presentations/coupled-oscillators)\]

**SEE ALSO**Double Spring Oscillation simulation### OHP Coupled Oscillators

\[S | t+ | —\]  
Magnetically coupled oscillators which can be driven to show two normal modes of vibration; one oscillator can also be tuned.

### Three Coupled Oscillators

\[S/M | t+ | —\]  
Three hacksaw blade oscillators electromagnetically driven to demonstrate three normal modes of vibration.

### Air Track Coupled Oscillators

\[L | t+ | —\]  
Two or more gliders, coupled by springs, driven to show normal modes of vibration.

### Synchronization of Metronomes

\[M | t+ | ★★★★\]

\[[In-Depth Description](/presentations/synchronization-metronomes)\]

### Non-linear Oscillations

\[L | t++ | —\]  
Air track glider/oscillator with a spring arrangement so that restoring force is proportional to (displacement) 2.

### Chaotic Pendulum

\[M | t | ★★★\]  
Coupled, double, physical pendulum executes chaotic motion when non-linear initial conditions are imposed.

\[[In-Depth Description](/presentations/chaotic-pendulum)\]

### 'Y' Suspended Pendulum

\[M | t | —\]  
Pendulum with two distinct periods...superposition of normal modes of oscillation.

### Sand Pendulum

\[L | t+ | —\]  
Pendulum leaks sand onto black paper leaving a record of rotating ellipsoidal motion.

### Ellipsometer

\[M | t+ | —\]  
Physical pendulum with analog x and y displacement readout on storage oscilloscope.

### Shattering Wineglass

\[L | t+ | ★★★★\]  
Large speaker with signal generator/amplifier destroys a wineglass; stroboscopic illumination shows vibration mode.  
  
\[[In-Depth Description](/presentations/shattering-wineglass)\]

### Barton's Pendulum

\[L | t | ★★★★\]  
Ten coupled pendulums of different lengths; shows resonance and phase.  
  
\[[In-Depth Description](/presentations/bartons-pendulum)\]

### Chladni Plates

\[S | t+ | ★★★★\]  
Accumulation of sand at nodes of vibrating plate reveals resonance patterns.  
  
\[[In-Depth Description](/presentations/chladni-plates)\]

### Big Chladni Plate

\[L | t++ | ★★★ \]  
Electromagnetically driven plate to show two dimensional modes of vibration.

\[[In-Depth Description](/presentations/big-chladni-plate)\]

### Vibrations on a Drumhead

\[— | — | —\]  
A driven membrane to show modes of vibration.  
  
\[[In-Depth Description](/presentations/vibrations-drumhead)\]

### Frahm Resonance Gyroscope

\[S | t | ★★\]  
Vibrational resonances of metal reeds are excited by a spinning gyro as it slows down  
  
\[[In-Depth Description](/presentations/frahm-resonance-gyroscope)\]

### Parametric Excitation

\[M | t+ | —\]  
A pendulum is set into motion by periodically pulling on the string at the proper frequency

### Inverted Pendulum

\[S | t+ | ★★★\]  
A physical pendulum finds stability in its inverted position when driven at the proper frequency and amplitude combination.  
  
\[[In-Depth Description](/presentations/inverted-pendulum)\]

### Rotating Saddle

\[L | t | ★★★★\]  
Mechanical analog of a Paul Trap particle confinement - a ball is trapped in a time-varying quadrupole gravitational potential.  
  
\[[In-Depth Description](/presentations/rotating-saddle)\]

### Dust Particle Paul Trap

\[S | t+ | —\]  
An electrically charged dust particle is trapped in a time-varying (60 Hz) quadrupole electric field.

### Contact Us

**Mailing Address**: Lecture Demonstration Services, Science Center, Rm B-08A, 1 Oxford Street, Cambridge, MA 02138  
**Campus Location**: Science Center B-08A | **Tel**: (617) 495-5824 | **Email**: scidemos-at-fas.harvard.edu