Sums of Sinusoidal Forces or EMF’s—Fourier Analysis
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.
KeywordsFourier Series Fundamental Period Fourier Integral Integral Diverge Spective Exponent
Unable to display preview. Download preview PDF.
- 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