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Solving Forced Oscillator Differential Equations Using the Exponential Response Formula
The exponential response formula (ERF) is a shortcut for finding one particular solution to a forced oscillator differential equation, such as x'' + 8x = cos(wt). You use it when a constant-coefficient equation is pushed by a cosine or sine input. The trick is to rewrite the cosine as the real part of a complex exponential, apply the formula, and take the real part of the answer. The ERF belongs to the study of linear differential equations and forced vibrations.