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Oscillations II

In: Modern Analytic Mechanics

Author

Listed:
  • Richard K. Cooper

    (Formerly of Los Alamos National Laboratory)

  • Claudio Pellegrini

    (University of California at Los Angeles)

Abstract

We consider now a system consisting of an elastic string to which N particles, each of mass m, have been attached. We assume the particles to be equally spaced along the string, with a separation d,so that the total length of the string is L = (N + 1)d. The loaded string is a good example of a system with many degrees of freedom. In fact we will show that we can explicitly find the eigenvalues and eigenvectors of this system for an arbitrary number N of particles. The loaded string is also a good introduction to the case of the vibration of a continuous string and one-dimensional waves in a mechanical system, which we will study in the next chapter.

Suggested Citation

  • Richard K. Cooper & Claudio Pellegrini, 1999. "Oscillations II," Springer Books, in: Modern Analytic Mechanics, chapter 0, pages 121-146, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-5867-2_6
    DOI: 10.1007/978-1-4757-5867-2_6
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