3 ms·

Natural frequencies of mechanical systems are eigenvalues of it’s equation of motion.

• _spduchamp 4y ago
  Any references to help me unpack what you just said there?
  • sfpotter 4y ago
    Things that vibrate have natural modes of vibration. A particular vibrational pattern can be decomposed into a time-varying linear combination of these modes. The modes of vibration are eigenfunctions and the frequencies at which they vibrate are the square root of the corresponding eigenvalues. You can look up a vibrating drum head (circular membrane) for a simple example.
  • wolfi1 4y ago
    Landau/Lifshitz: "Mechanics" has a chapter on small oscillations
    • pvg 4y ago
      That's more of a further packing than an unpacking. Although that totally should be an expression for things that go on for too long: "Can you pack this for me please"
  • bumby 4y ago
    Theory of Vibration with Applications by William Thompson and Marie Dillon Dahleh. Say you have two cars linked, with some spring constant; | --^^-- [c1] --^^-- [c2] --^^--| where '^^' is a spring and '|' is a wall. The motion of these cars can be written using the spring forces in the system or, alternately, as the harmonic motion of the undamped system with some natural frequency. Setting this up as two simultaneous equations (one for each car) and solving for the roots give you the eigenvalues. The natural frequency is the square root of the eigenvalue. In other words, the eigenvalues help you define the natural frequencies which can be used to characterize the motion of the cars in the more complicated spring-mass system.