Question

Find the first 2 harmonics of the Fourier series for the values given in the following table: t 60° 90° 180° 270° 0° f(t) 3.1

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Sol:- A8 we know that, fourier senes f(x) = at a láncosnx + bn Sinor) nal = a + a, cosxt bisina ta e cos2x+ 1st harmonic 2ndfor 18+ harmonic a 2 Efalcosa b. Eflx) sina Page No. Date 2 and for 2 nd harmonic 12 - 2 Eflat cos ex N 22 о & Efxl sinarPage No. BR (Date: 11 Now in this question a table of + and tt) is given, so FOOD this table we find Eflx) cosx = Eflt cost,Page No. Date: So, Ast harmonic a, cost tb, sint a, a 2 E ft) cost 12 2 10 20 be h Eftt) sint 2. PAKOJ here in toms of to =xHence the first 2 harmonic Of the fourier series is O, 0.525 cos 2t - 0.906 sinat t fa 1st harmonic and harmonic

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