Confusion about two modes of coupled oscillators having same frequency

Click For Summary
SUMMARY

In the discussion regarding coupled oscillators, it is established that two modes can indeed have the same natural frequency if there are repeated roots in the characteristic equation. This scenario, while possible, is uncommon and typically occurs in special cases where the modes are independent, meaning there is zero coupling between them. The confusion arises from differing references, with one source affirming the possibility and another denying it based on the coupling conditions.

PREREQUISITES
  • Understanding of coupled oscillations
  • Familiarity with characteristic equations
  • Knowledge of natural frequency concepts
  • Basic principles of linear algebra
NEXT STEPS
  • Study the derivation of characteristic equations in coupled oscillators
  • Explore examples of repeated roots in oscillatory systems
  • Investigate the effects of coupling on natural frequencies
  • Review literature on independent modes in oscillatory systems
USEFUL FOR

Students and researchers in physics, particularly those focusing on oscillatory systems, as well as educators seeking to clarify concepts of coupled oscillations and natural frequencies.

PrathameshR
Messages
35
Reaction score
3
I am studying coupled oscillations and one of the refrance I'm using says that two modes can have same frequency whereas the other one says it's impossible to have same frequency for two modes. Please help.
20180321_193658-1.jpeg
20180321_193903-1.jpeg
 

Attachments

  • 20180321_193658-1.jpeg
    20180321_193658-1.jpeg
    45.1 KB · Views: 863
  • 20180321_193903-1.jpeg
    20180321_193903-1.jpeg
    73.3 KB · Views: 822
Physics news on Phys.org
For two modes to have the same natural frequency there must be repeated roots for the characteristic equation. This can happen although it is not very common in my experience.
 
The example in the first book seems to be a special case where the x,y modes considered are independent of each other—the coupling is zero. Confirmation of that would be on previous pages that we can’t see.
 

Similar threads

Undergrad Two molecules with different polarizability in an EM field
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Error tolerant normal mode frequency
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Pair of interacting systems, driven coupled harmonic oscillators
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Off resonance driving of a MW/RF cavity
  • · Replies 9 ·
Replies
9
Views
1K
Graduate Relating resonant frequency to electrical impedance
  • · Replies 9 ·
Replies
9
Views
2K
High School Ion Trap and Time-Varying Potentials
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Antenna made from a pair of metal cones, radiation gain verses frequency.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Need a good idea : 3D simulation of Inductive wireless power transfer
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Why different cutoff frequencies for TE and TM in a medium?
  • · Replies 1 ·
Replies
1
Views
2K
High School Antenna induction, oscillating circuit generating EM Waves
  • · Replies 6 ·
Replies
6
Views
2K