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17 Apr How can you use Fourier series to solve a differential equation? For an example, look at the forced harmonic oscillator. If the forcing function is periodic, you can write it using a series of functions that satisfy periodic boundary conditions.
Here w = 2p/T and T is the period of the applied force. If you try to solve the equation
the first step will be to solve the inhomogeneous equation for one of these terms in the Fourier series, then to add the results. The result is a series representation of the solution for x( t ). This solution has the notable property that if the natural frequency of the oscillator coincides with any one of the harmonics of the forcing function, then you get resonance.
