. Graphical and mechanical computation . -Si sin 75°+56 s n30° — s3 sin 450+54 sin 60°+^ sin 75° —s6 s (di — d3 — d5) sin 450 — d4s — (di — d3 — d5) sin 450 — \ + fls + as + a? + «9 + an = o,61 - 63 + b-0 - b7 + 69 - 6n = y6. y = a,\ cos x + az cos 3 .%+•• • + On cos 11 x+ bi sin x + 63 sin 31 + ? ? ? + Fig. 90&. Example. Fig. 906 represents a half-period of an wave whosefrequency is 60 cycles. We wish to find the odd harmonics up to the nthorder. Choose the x-axis midway between the highest and lowest pointsof the complete wave and the origin at the point where the wave cross
. Graphical and mechanical computation . -Si sin 75°+56 s n30° — s3 sin 450+54 sin 60°+^ sin 75° —s6 s (di — d3 — d5) sin 450 — d4s — (di — d3 — d5) sin 450 — \ + fls + as + a? + «9 + an = o,61 - 63 + b-0 - b7 + 69 - 6n = y6. y = a,\ cos x + az cos 3 .%+•• • + On cos 11 x+ bi sin x + 63 sin 31 + ? ? ? + Fig. 90&. Example. Fig. 906 represents a half-period of an wave whosefrequency is 60 cycles. We wish to find the odd harmonics up to the nthorder. Choose the x-axis midway between the highest and lowest pointsof the complete wave and the origin at the point where the wave crossesthe x-axis in the positive direction. Divide the half-period into 12 equal Art. 90 NUMERICAL EVALUATION OF THE COEFFICIENTS 191 parts and measure the ordinates yi, y% . . , yn. These are given inthe following table:x 15° 30° 45° 6o° 75° 900 105° 120° 135°50 150030 4 21 19 27 29 33 46 38 We arrange the work in the above computing form. 4 21 19 27 29 33 37 + 69 - 75 = 31 = n 33 3Q 50 38 46 51 - 33 Sums (s) 37 51 69 65 75 33Diff. (ef) —29— 9 —31 —11 —17 = 18 = r2-29 + 31 -- 17 = 19 = ei Multipliers Cosine terms Sine terms Sum 1st
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