Eigenfrequencies of couple oscillators

Click For Summary
The discussion centers on the eigenfrequencies of a system with two masses connected by springs, where the calculated frequencies are found to be imaginary. Participants explore the implications of non-real frequencies, suggesting that imaginary frequencies indicate exponential behavior rather than simple harmonic motion. The conversation touches on the relationship between imaginary frequencies and damping effects in oscillatory systems. This leads to the conclusion that while imaginary frequencies can occur, they signify a different type of motion than typical oscillations. Understanding these concepts is crucial for analyzing the dynamics of coupled oscillators.
CanIExplore
Messages
97
Reaction score
0

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.
 
Last edited:
Physics news on Phys.org
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:
 

Similar threads

Undergrad Error tolerant normal mode frequency
  • · Replies 7 ·
Replies
7
Views
2K
Small oscillations and a time dependent electric field
  • · Replies 4 ·
Replies
4
Views
2K
Small oscillations on a constraint curve
  • · Replies 5 ·
Replies
5
Views
7K
Can Eigenfrequencies Explain Oscillatory Behavior in this Dynamical System?
  • · Replies 3 ·
Replies
3
Views
3K
Finding the normal modes for a oscillating system
  • · Replies 4 ·
Replies
4
Views
2K
Eigenvalues and vectors of a 4 by 4 matrix
  • · Replies 3 ·
Replies
3
Views
3K
What are the simple modes and frequencies for weakly coupled oscillators?
  • · Replies 4 ·
Replies
4
Views
2K
How Do You Formulate the Lagrange Function for a Triatomic Molecule Model?
  • · Replies 2 ·
Replies
2
Views
4K
A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x)....
  • · Replies 3 ·
Replies
3
Views
5K
Find the possible total energies (Quantum Physics)
  • · Replies 7 ·
Replies
7
Views
2K