Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...into 6 equal parts, and measure the 5 ordinates yu yi' y3, y4, y&. Thus we have-r e--I500 The following example will illustrate the rapidity with which the coefficients may be determined. Example. We wish to analyze the symmetric wave of Fig. 90a, i.e., to find the coefficients of the 1st, 3d, and 5th harmonics. Choose the x-axis midway between the highest and lowest "points of the wave, and the origin at the point where the wave crosses this axis in the positive direction. Then divide the half-period into 6 equal parts and measure the ordinates yu..., yb. These are given in the following table: Result: y =--5.65 cos x + 7.90 cos 3 #--2.25 cos 5 x + 19.84 sin x + 2.27 sin 3 x + 2.93 sin 5 x. (II) Odd harmonics up to the eleventh.--Given a symmetric curve and wishing to determine the coefficients in the equation y = ai cos x + a3 cos 3 x + + On cos 11x + bi sin x + b3 sin 3 x +. + bn sin 11x, we choose the origin at the point where the wave crosses the axis, so that yo = o divide the half-period into 12 equal parts, and measure the 11 ordinates yu y2,..., yn. Thus we have 165 yn For the coefficients we have the following equations: 6 ai = yi cos 150 + y2 cos 300 + + yn cos 1650 6a3 = yi cos 450 + y2 cos 900 + + yn cos 4950 Example. Fig. gob represents a half-period of an e.m.f. wave whose frequency is 60 cycles. We wish to find the odd harmonics up to the nth order. Choose the x-axis midway between the highest and lowest points of the complete wave and the origin at the point where the wave crosses the x-axis in the positive direction. Divide the half-period into 12 equal Check: ai+as+ 6i-k4-Result: y =--11.27cosx + 4.07cossx 4-0.05cos5x 4-0.72cos7x--0.40cos9x + 6.83 cos Iix4-40.95 sin x + 6.65 sin 3 x + 142 sin 5 x 4-0.68 sin 7 x + 0.65 sin 9 x 4-2...
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