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    Fourier Expansion

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    Assume a Fourier expansion of the form [see the attachment for equation] and determine the coefficients b_n(t). The initial conditions are [see the attachment for equations].

    Note. This is only half the conventional Fourier orthogonality integral interval. However, as long as only the sines are included here, the Strum-Liouville boundary conditions are still satisfied and the functions are orthogonal.

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    This solution provides steps to determine the coefficients.