Eigenfrequencies of couple oscillators

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SUMMARY

The discussion centers on the eigenfrequencies of a system consisting of two masses, each connected by springs with constants 2k, 4k, and k. The participant has calculated eigenfrequencies that are imaginary, raising questions about the implications of non-real frequencies in oscillatory systems. It is confirmed that imaginary frequencies indicate exponential behavior in the system, suggesting that the oscillations do not correspond to stable harmonic motion.

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  • Understanding of classical mechanics, specifically oscillatory motion
  • Familiarity with eigenvalue problems in linear algebra
  • Knowledge of spring constants and their role in harmonic systems
  • Basic concepts of complex numbers and their applications in physics
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  • Study the implications of imaginary eigenfrequencies in mechanical systems
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Homework Statement


I have solved for the eigenfrequencies of a system composed of two particles of masses m connected to each other by a spring of constant 2k and where one particle is connected to a wall by a spring of constant 4k and the other particle is connected to a second wall by a spring with constant k. The particles are restricted to move along the line containing all three springs.

Homework Equations


The Attempt at a Solution


I have obtained the eigenfrequencies already but they came out to be imaginary. I am wondering what it means for a frequency to be non real, or if it is even possible to have such an imaginary frequency.
 
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Hi CanIExplore! :smile:
CanIExplore said:
I have obtained the eigenfrequencies already but they came out to be imaginary. I am wondering what it means for a frequency to be non real, or if it is even possible to have such an imaginary frequency.

Sounds like they're exponential …

eikt is shm …

imaginary k corresponds to ekt or e-kt :wink:
 

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