Eigenfrequencies of couple oscillators

In summary, the conversation discusses solving for the eigenfrequencies of a system with two particles connected by springs and restricted to move along a line, with one particle connected to a wall and the other connected to a second wall. The attempt at a solution resulted in imaginary eigenfrequencies, leading to a discussion about the meaning and possibility of having imaginary frequencies in the context of exponential functions.
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CanIExplore
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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:
 

1. What are eigenfrequencies in the context of couple oscillators?

Eigenfrequencies refer to the natural frequencies at which a system oscillates without any external force applied. In the case of couple oscillators, these are the frequencies at which the two oscillators are coupled and vibrate in unison.

2. How do eigenfrequencies affect the behavior of couple oscillators?

The eigenfrequencies determine the overall behavior of couple oscillators. When the eigenfrequencies of both oscillators are the same, they will oscillate in phase and amplify each other's oscillations. However, if the eigenfrequencies are different, the oscillators will be out of phase and their vibrations will cancel each other out.

3. What factors can affect the eigenfrequencies of couple oscillators?

The eigenfrequencies of couple oscillators are affected by the stiffness of the springs connecting the two oscillators, the masses of the oscillators, and the strength of the coupling between them. Changes in any of these factors can alter the eigenfrequencies and consequently change the behavior of the system.

4. How can we calculate the eigenfrequencies of couple oscillators?

The eigenfrequencies can be calculated using mathematical equations that take into account the factors mentioned above, such as the masses, stiffness, and coupling strength. These equations can be solved using techniques like matrix diagonalization or numerical methods.

5. Can the eigenfrequencies of couple oscillators be manipulated?

Yes, the eigenfrequencies can be manipulated by changing the parameters of the system, such as the masses, stiffness, and coupling strength. This can be useful in designing oscillators with specific behaviors or in controlling the vibrations of a system.

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