Fourier Analysis
The principle of superposition can be used to understand an arbitrary wave form
Jean Baptiste Fourier (1786-1830) showed that an arbitrary wave form can be written as a sum of a large number of sinusoidal waves with carefully chosen amplitudes and frequencies
e.g. y(0,t)= -(1/?) sin(?t)-(1/2?) sin(2?t) -(1/3?) sin(3?t)-(1/4?) sin(4?t)-...
Decomposition into sinusoidal waves
is analogous to vector components