The Physics of Oscillations and Waves pp 51-72 | Cite as

# Sums of Sinusoidal Forces or EMF’s—Fourier Analysis

Chapter

## Abstract

In Chapter 3 we studied the response on an oscillator to a driving force with sinusoidal time-dependence. In the present chapter we build up more complicated forces by adding sinusoidal forces together.

## Keywords

Fourier Series Fundamental Period Fourier Integral Integral Diverge Spective Exponent
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## Notes

- 1.Some authors generalize the definition of orthogonality by including in the integrand of Equation 4.3 an additional factor
*w(t)*,known as a “metric” or a “weighting” function. See, for example, Arfken, G.*Mathematical Methods for Physicists*. 2d ed. New York: Academic Press, 1970. Morse, P. M. and H. Feshbach.*Methods of Theoretical Physics*. New York; McGraw Hill, 1953.Google Scholar - 2.We state many mathematical results without proof. Proofs can be found in books on mathematical analysis, such as E. T., Whittaker, and G. N. Watson.
*A Course of Modern Analysis*. American ed, New York; Macmillan, 1943.Google Scholar - 3.Mathematical analysis has been extended to include nonfunctions such as the delta “function,” which is called a “distribution” instead of a function. The branch of analysis that deals with such objects is known as the theory of distributions. It is discussed in Barros-Neto, J.
*An Introduction to the Theory of Distributions“ New York; Dekker*,1973. Challifour, J. L.*Generalized Functions and Fourier Analysis; an Introduction*. Reading, MA; Benjamin, 1972.Google Scholar - 4.Useful general references on Fourier analysis are: Churchill R. V. and J. W. Brown.
*Fourier Series and Boundary Value Problems*, 3d ed. New York: McGraw Hill, 1978. Campbell, G. A. and R. M. Foster.*Fourier Integrals for Practical Applications*. New York; Van Nostrand, 1947.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1997