Classical Dynamics of Particles and Systems · Problem 3-28

Nonlinear Oscillations and Chaos — Marion & Thornton

Physics — Mechanics · fourier-series

Problem

Obtain the Fourier expansion of the function F(t)={−1,−π/ω<t<0+1,0<t<π/ωF(t) = \begin{cases} -1, & -\pi/\omega < t < 0 \\ +1, & 0 < t < \pi/\omega \end{cases} in the interval −π/ω<t<π/ω-\pi/\omega < t < \pi/\omega. Take ω=1\omega = 1 rad/s. In the periodical interval, calculate and plot the sums of the first two terms, the first three terms, and the first four terms to demonstrate the convergence of the series.

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