What is Eigenfrequencies: Definition and 11 Discussions

In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by



λ


{\displaystyle \lambda }
, is the factor by which the eigenvector is scaled.
Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.

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  1. aligator11

    Engineering Homework problem - Pendulum oscillatory system

    Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.
  2. A

    Eigenfrequencies of a multiple DOF system

    I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...
  3. S

    Why are we only considering the first eigenfrequencies?

    Hey, I have a question concerning eigenfrequencies: Let us assume we examine a beam that is fixed at one end and free at the other end. It is possible to get an analytical solution in form of a unlimtied series: sum_i=1..infinity eigenfunction(i)*exp(i*eigenfrequencie(i)*t). (something...
  4. S

    I Normal Modes: Finding Eigenfrequencies

    If I have a system where the following is found to describe the motion of three particles: The normal modes of the system are given by the following eigenvectors: $$(1,0,-1), (1,1,1), (1,-2,1)$$ How can I find the corresponding eigenfrequencies? It should be simple... What am I missing?
  5. B

    Why do unsupported beams have eigenfrequencies?

    I know that a beam suspended in two ends can have many modal shapes. However, when it comes to unsupported free beam its first three eigenfrequencies are 0, why? And why should it have eigenfrequencies at all if it is free to move? Is eigenfrequency characteristic of every material? Why is it...
  6. S

    Why Do Bounded Mediums Have Specific Eigenfrequencies?

    in waves and oscillations i read that any bounded medium oscillates in a particular freuency...why is it so?i need a proper reason for this
  7. M

    Finding eigenfrequencies of a coupled pendulum

    Homework Statement This problem is from the 1992 GRE. A tube is free to slide on a frictionless wire. On each end of the tube is attached a pendulum. The mass of the tube is M. The length and mass of the pendula are l and m, respectively. Homework Equations It is given that one of the...
  8. C

    Eigenfrequencies of couple oscillators

    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...
  9. X

    Normal modes / Eigenfrequencies

    1. Homework Statement Someone studying a dynamical system in another field of science tells you that when they attempt to model the experiment they’ve been examining they obtain the following set of coupled ordinary differential equations. \dot{x}= -Ax + By \dot{y}= -Cx In what follows you...
  10. R

    Find the eigenfrequencies for systems

    Homework Statement (M + m) \ddot x + m l \ddot\theta - ml \dot\theta ^2\theta = 0 \ddot\theta + \frac{\ddot x}{l} + \frac{g}{l}\theta = 0 I am not quite sure how to get a x(t) and theta(t) that actually fit for these equations... For the second equation, I was thinking something like x(t) =...
  11. qspeechc

    How Does a Magnetic Field Affect Eigenfrequencies in a Harmonic Oscillator?

    Homework Statement Hello everyone. I'm trying to find the eiegenfrequencies in a problem. We have a particle of mass m, charge e, that is subject to a linear restoring force \textbf{F} = -k\textbf{r} and the particle is in a magnetic field [tex]\textbf{B} = B\textbf{k}[/itex] (in the...
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