Complex harmonic motion is the superposition - linear combination - of several simultaneous simple harmonic motions.
Complex harmonic motion is periodic, and can be analyzed through the techniques of harmonic analysis discovered by Fourier.
Examples of complex harmonic motion are musical chords, Lissajous curves, and finite partial sums of Fourier series. The harmonograph is approximately (or when considering friction as negligible) governed by a complex harmonic motion.
In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalisations given at the end of the article.
In a given situation, K and V may be specified explicitly, or they may be obvious from context. In that case, we often speak of a linear combination of the vectors v1,...,vn, with the coefficients unspecified (except that they must belong to K).
Or, if S is a subset of V, we may speak of a linear combination of vectors in S, where both the coefficients and the vectors are unspecified, except that the vectors must belong to the set S (and the coefficients must belong to K). Finally, we may speak simply of a linear combination, where nothing is specified (except that the vectors must belong to V and the coefficients must belong to K).
Home Page