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.
KeywordsAnharmonic Oscillator Stable Fixed Point Paraxial Approximation Angle Figure Unstable Equilibrium Point
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