Coupled Oscillations
Keith Arnold, John Filaseta
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Reference Antisymmetric Mode Both carts at
maximum from reference Symmetric Mode Cart # 1 at
maximum from reference Cart # 2 at
minimum from reference Reference
Coupled Oscillations occur when two or more oscillating systems are connected in such a manner as to allow motion energy to be exchanged between them. Coupled oscillators occur in nature (e.g., the moon and earth orbiting each other) or can be found in man-made devices (such as with the pacemaker).
Consider two identical cart masses connected in motion by springs (two end springs, one middle spring). The photo’s above were taken when the carts were oscillating in their normal modes (i.e., the symmetric mode and the antisymmetric mode). Normal modes occur when both carts oscillate at the same frequency. You can see a video of these normal mode oscillations by clicking on each of the photo’s above.
Data:
Each cart mass = 0.214 kg.
Each end spring constant = 2.90 N/m.
Middle spring constant = 1.635 N/m.
Ways to find the periods of
oscillations for the normal modes:
- Solve the coupled differential equations found from applying
- Observe the moving carts on video and count frames (12 frames per second).
- Measure the period from plots obtained with motion sensors.
View video for symmetric mode of oscillations.
View video for antisymmetric mode of oscillations.
View plot for antisymmetric mode.
After finding the periods, you can compare your result to the answers found here.