A voltage is periodic with period

PHYSICS · Multi-part · 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 voltage v(x)v(x) is periodic with period LL. Within one period, −L/2<x≤L/2-L/2 < x \le L/2, it is a single rectangular pulse of height h=5.00 Vh = 5.00\,\mathrm{V} centred on the origin, of width L/4L/4: v(x)={5.00 V,−L/8<x<L/80,otherwise, for −L/2<x≤L/2v(x) = \begin{cases} 5.00\,\mathrm{V}, & -L/8 < x < L/8 \\ 0, & \text{otherwise, for } -L/2 < x \le L/2 \end{cases} and v(x+L)=v(x)v(x+L)=v(x) for all xx. ((a)) Compute a0a_0. ((b)) Compute a1a_1. ((c)) Compute a2a_2.

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