Oscillations II

  • Richard K. Cooper
  • Claudio Pellegrini


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.


Anharmonic Oscillator Stable Fixed Point Paraxial Approximation Angle Figure Unstable Equilibrium Point 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Richard K. Cooper
    • 1
  • Claudio Pellegrini
    • 2
  1. 1.Formerly of Los Alamos National LaboratoryLos AlamosUSA
  2. 2.University of California at Los AngelesLos AngelesUSA

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