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. 1905 edition. Excerpt: ...1842. Art. 278. 326. To find the Forced Vibration. To find a particular integral for any force Pe'Kt sin (Xt + a) we follow the ...
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. 1905 edition. Excerpt: ...1842. Art. 278. 326. To find the Forced Vibration. To find a particular integral for any force Pe'Kt sin (Xt + a) we follow the methods already explained in Chap. VI. If A (8) be the determinant of the motion and /, (6"), 12 (&), &c. be the minors of the first, second, &c. terms in that row of A (8) which corresponds to the equation in which the force occurs, we have x = )Pe-Kt8m(Xt + a), y = Pe-'sin(i4-a), = &c. We shall now prove that these operators lead to two trigonometrical terms in each of the coordinates. These two terms constitute the forced vibration in that coordinate. 327. To perform the operations indicated by these functions of S, we use the following simple rule. To perform the operation F(S) = on PeKt 8ia (t + o) we A (5J cosv' write 6=-K + s/-I and reduce the operator to the form L + M J-1. The required result is then PeKt(L + H-) S1 (t + a). X/cos To prove this rule, we notice that, by Art. 265, F (J) emt= (L + If N/-1) emt where m=-Ac + X N/-1. If we now replace the imaginary part of the exponential by its trigonometrical value, and equate the real and imaginary parts on each side of the equation, the result follows at once. 328. If the force is permanent K = 0 and it immediately follows that the consequent forced vibration is also permanent. 329. If the determinant A(i) have a roots each equal to m, i.e.-k + Xz-i, the result assumes an infinite form. In this case the operator may be replaced by taI(S) + ata-1r(S) +...+la(S)la(S), where the coefficients follow the binomial law, and Aa(5), &c. have been written to express the ath differential coefficient of A (S), &c. Every one of these operations may now be performed by the rule given in the last article. To prove this, we replace the root m by m +...
Very Good. 8vo-over 7¾"-9¾" tall. 484 pp. Tightly bound. Spine not compromised. Book plate from "The Franklin Institute Library" on the front paste down. Call number on spine. A check out slip on back paste down. No other library stamps, pockets or markings. A very clean ex-library copy. NOTE: This is the 1955 DOVER EDITION.
Good. "Property of Technical Library Naval Missile Center, Point Mugu, California" stamped on front loose end pages, outer edges of pages and inside back cover. Library pocket inside back cover. NO DJ. 1955. We have 1.5 million books to choose from--Ship within 48 hours--Satisfaction Guaranteed!
Good/Wraps. Trade paperback, good condition, w. ltly rubbed wraps, sme lt marks. Lt tanning, a few lt spots on r. Smwht tanned p. edges, sme lt soil or spots. V. ltly tanned ins wraps, ltly tanned pp. Clean, tight, unmarked.
Good. Used Paperback. Sixth edition. Covers are marked. Leading corners, edges and spine are worn and scored. Two centimetre tear on spine head; nicks on spine foot. Page block is a little grubby. Previous owner's name penned on front inside cover. Staples are visible on inside covers. A few minor marks on last pages. Binding is intact, contents are clear. AM.
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