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. 1821 Excerpt: ...at what distance a moveable point must be situated before or behind it, in order to represent the actual magnitude of the periodical force by the relative situation, according to the law of the primary force concerned, and to find an expression for this distance in terms of the sines of arcs increasing equably, in ...
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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. 1821 Excerpt: ...at what distance a moveable point must be situated before or behind it, in order to represent the actual magnitude of the periodical force by the relative situation, according to the law of the primary force concerned, and to find an expression for this distance in terms of the sines of arcs increasing equably, in order to obtain the situation and velocity of the body at any time, provided that we suppose it to have attained a permanent state of vibration. Scholium 3. We may easily express this reasoning in a form more strictly algebraical: thus the time, with respect to the forced vibration of the centre of suspension, being called t, the place of the vertical line passing through that point will be indicated by sinf, supposing t to begin from the middle of a vibration: now the force acting on the moving body will always be as its distance from this moveable vertical line, considered with relation to the length of the true pendulum m; that is, it will be expressed g SIn t byf=, the unit of m being the length of the imagi Til nary pendulum carrying the point of suspension, since when a=0 and sin t--, the force must be=l or=g. Now we may satisfy this equation by the particular solution s--sin t--a sin t, which represents a vibration either corresponding in its direction with the former, or in an opposite direction, accordingly as a is positive or negativeand s, the space actually described, will be the sum or difference of the spaces belonging to the separate vibrations so combined: then since v----f fdt, and s = fv&t, we have that, at the middle of a vibration, the point of suspension (A) be so situated, as to cause a propelling force equal to the actual resistance, the extent of the vibrations being reduced, in the ratio of the whole excursion of the p...
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New. Sewn binding. Cloth over boards. 354 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
