Oscillations of Mechanical and Electrical Systems

  • Stephen Nettel
Part of the Advanced Texts in Physics book series (ADTP)


The equation of motion for a mechanical system comprised of a mass at the end of a string and vibrating in a viscous medium is compared to the analogous equation for an electrical system consisting of an R-L-C circuit. The distinction between natural and driven dynamics is carefully drawn. For natural motion the initial value problem is solved for the case of negligible viscous damping, negligible electrical resistance. The resonance phenomenon is brought out fully in connection with the analysis of forced motion, and the characteristics of resonance are related to those of natural motion, attention being drawn to the quality factor Q. The Green’s function method of finding the solution for forced motion is described. A subsequent section is then devoted to an explanation of the operation of oscillators in general, and extended to a description of an actual pendulum clock. In the problems we treat natural motion for nonnegligible damping.


Mechanical System Mechanical Analogue Electrical System Suspension Bridge Viscous Medium 
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Further Reading

  1. R. Resnick, D. Halliday: Physics, Vols. I and II (Wiley, New York 1977 ) An introduction to harmonic oscillators is given in these volumes.Google Scholar
  2. I.G. Main: Vibrations and Waves in Physics ( Cambridge University Press, Cambridge 1978 )MATHGoogle Scholar
  3. P.R. Wallace: Mathematical Analysis of Physical Problems ( Dover, New York 1984 )MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stephen Nettel
    • 1
  1. 1.Department of PhysicsRensselaer Polytechnic InstituteTroyUSA

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