Items related to Graphical and Mechanical Computation
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: ...+ + bn sin 11 x, we choose the origin at the point where the wave crosses the axis, so that yo = 0, divide the half-period into 12 equal parts, and measure the 11 ordinates yu yi yn. Thus we have 165 yu For the coefficients we have the following equations: 6 ai = yi cos 150 + y2 cos 300 + + yn cos 1650. 6ai = yi cos 450 + y2 cos 900 + + yn cos 4950. Example. Fig. 906 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 parts and measure the ordinates yi, yi..., yn. These are given in the following table: sum of the amplitudes, taken alternately plus and minus, of the nth, 3 nth, 5 nth,... sine components. We arrange the work in the above computing form. 4 21 19 27 29 33 37 + 69-75 = 31 = n 33 30 50 38 46 51-33 = 18 = r2 Sums (s) Check: ai+a3 + bl-b3+ Result: y =--11.27 cos x + 4.07 cos 3 x + 0.05 cos 5 x + 0.72 cos 7 x--0.40 cos 9 x + 6.83 cos 11 x + 40.95 sin x + 6.65 sin 3 x + 1.42 sin 5 x + 0.68 sin 7 x + 0.65 sin 9 x + 2.68 sin 11 x. (Ill) Odd harmonics up to the seventeenth.--Given a symmetric curve and wishing to determine the coefficients in the equation y = ai cos x + a3 cos 3 x + + an cos 17 x + bi sin x + b3 sin 3 x + + bii sin 17 x, we choose the origin at the point where the wave crosses the axis, so that yo = 0, divide the half-period into 18 equal parts, and measure the 17 ordinates ylt yi,..., y7. Thus we have If we use the same method as that employed in deriving the n-ordi; nate scheme, we shall arrive at the following 17-ordinate computing formj This form is s...
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- PublisherRarebooksclub.com
- Publication date2012
- ISBN 10 113036335X
- ISBN 13 9781130363357
- BindingPaperback
- Number of pages30
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