Coupled Harmonic Oscillators - Multiresonant Systems

References

Dan Russell's Acoustics and Vibration Animations

The Physics Classroom

Derivation of Wave Equation - Beaded String

Sound Waves - ISVR Teaching Materials on Waves and Acoustics

Physics Java Applets by C. K. Ng

Examples of Coupled Mechanical Oscillators


                                
symmetric mode                        antisymmetric mode
(source)                                 





                 

(source)                                                                                                     (source)

(source)            s

(source)           

For more on standing waves on strings see C. K. Ng's Generate wave on a bounded string



Oscillators with More Than One Degree of Freedom

(taken from Dan Russell's Multiple DOF Systems)



           







Galloping of the Tacoma Narrows Bridge (1940)

Destructive coupling of transverse and torsional modes

(source)


Click on image for a
684KB movie
(source)

Click on image for a
7.5MB movie
(source)