Normal mode and eigenfrequency

In summary, the difference between eigenfrequency and normal mode is that the normal modes are the eigenvectors and the eigenvalues are also known as eigenfrequencies. In the example of solving the secular equation for a mechanical system, the eigenvalues represent the eigenfrequencies and the eigenvectors represent the normal modes. For two masses on a spring, the functions that describe the motion of the masses and their amplitudes of vibration are the normal modes, and each normal mode corresponds to a specific eigenfrequency. Additionally, there may be a transverse frequency for systems that oscillate when exposed to electromagnetic radiation, such as light.
  • #1
kaksmet
83
0
What is the difference between eigenfriquency and normal mode? If, for example, I solve the secular equation (from the equations of motion) for a mechanical system (say two masses on springs) to obtain the eigenvalues I thought I got the normal modes, but now I am told I get the eigenfrequencies..`?

Thanks for any help to enlighten me on this matter.

/K
 
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  • #2
The normal modes are the eigenvectors, the eigenvalues are what are also known as eigenfrequencies. Example Af=wf, where A is your operator (could be differential like d/dx etc), f is a function, w is the eigenvalue/eigenfrequency. If you solve this to find the functional form of f, then you have obtained the normal modes or eigenvectors as theyre also known. For each function f you find, you will also get a value of w...f1:w1, f2:w2 etc, these values of w are the eigenfrequencies.

So for the equations for two masses on a spring, the functions that describe the motion of the masses, and their amplitudes of vibration are your normal modes . To each of these normal modes will correspond a frequency of vibration, the eigenfrequency.
 
  • #3
nice explanation
 
  • #4
hey

It nice explanation :-)

I hve question.. what about the Transverse frequency, which systems ossillate if some electromagnetic radiations (e.g light) shines on the material.

Best regards
Abid
 

1. What is the difference between normal mode and eigenfrequency?

The normal mode of a system refers to the specific pattern of oscillation that occurs when the system is disturbed. Eigenfrequency, on the other hand, is the natural frequency at which the system will vibrate without any external input.

2. How are normal mode and eigenfrequency related?

The normal mode of a system is determined by its eigenfrequency. In other words, the eigenfrequency dictates the frequency at which the system will naturally vibrate, and the normal mode is the specific pattern of that vibration.

3. Can a system have multiple normal modes?

Yes, a system can have multiple normal modes, each with its own corresponding eigenfrequency. This is often seen in complex systems with multiple degrees of freedom.

4. How do normal mode and eigenfrequency affect resonance?

Resonance occurs when a system is driven at its eigenfrequency, resulting in a large amplitude response. Normal mode and eigenfrequency play a crucial role in determining the resonance behavior of a system.

5. How can normal mode and eigenfrequency be calculated?

The normal mode and eigenfrequency of a system can be calculated using mathematical equations that take into account the properties of the system, such as mass, stiffness, and damping. These equations are often solved using numerical methods or computer simulations.

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