A periodic driving force with period is stated directly as F(t) = 10.0 , N + 6.00 , N…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

A periodic driving force with period LL is stated directly as F(t)=10.0 N+6.00 Ncos⁡2πtL−4.00 Nsin⁡6πtL.F(t) = 10.0\,\mathrm{N} + 6.00\,\mathrm{N}\cos\frac{2\pi t}{L} - 4.00\,\mathrm{N}\sin\frac{6\pi t}{L}. Give the Fourier coefficients a0a_0, a1a_1, b1b_1, a3a_3 and b3b_3 of F(t)F(t) in the real form F=a02+∑n≥1(ancos⁡2πntL+bnsin⁡2πntL)F = \dfrac{a_0}{2} + \sum_{n\ge1}\left(a_n\cos\dfrac{2\pi nt}{L} + b_n\sin\dfrac{2\pi nt}{L}\right).

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