Proceedings of the Edinburgh Mathematical Society Volume 25-28.cEdinburgh Mathematical Society
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Author: Edinburgh Mathematical Society
Number of Pages: 116 pages
Published Date: 01 Mar 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
Format: eBook
ISBN: 9781130865578
Download Link: Proceedings of the Edinburgh Mathematical Society Volume 25-28
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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. 1907 Excerpt: ...other line EDO through E may be taken as a line of constraint, say of a thread fastened to the pendulum at D and to the vertical axis at O; but now the angular velocity n for this configuration must be changed so that (3) OF = X=y/n!, and the tension of the thread is Wsecf, where f denotes the angle EOF. Thus if AB is to be moved round the vertical by a support at B, the force must be applied along BE, and the angular velocity n must be such that (4) bo'= gin. The convertibility of C and L shows that the body can revolve at the same inclination about the vertical axis through L, and then the supporting thread at D must take the direction DE'O', and LO' must be the height of the equivalent conical pendulum. X. Experiment with a stick, whirled round at the end of a string). Draw Ce parallel to OE to meet the vertical through G in e, and draw fel horizontal; then (5) Co = E- = F/, C/=of = A.; 6 D-g4e=i'cg-gl=dg so that Dl is the pendulum length when D is the point of suspension, and then Cf is the height of the equivalent conical pendulum. Also OD DE n (7 CD = DG'CDDE = 0D-DG; the condition for steady motion, reducing for small value of S and f to (11) (A-Z)(A-a) = aA, the quadratic for A requisite in small conical motion, or is the plane oscillation seen side way, due either to a suspension by the thread DC, as in a boat hung from the davits, or to a forced vibration given by D, as a hand carrying a bag. If B had been the support, instead of D and on the opposite side of G, the sign of I and h must be changed, so that (12) (I + A)(a-A) = ah, or A2 + II-a)A-a(l-h) = 0, with l-h =-, h so that the quadratic for A has real roots; and this gives the condition for the balance of the rod AB on its lowest point B, by a thread of length Bo' = a. A small ci...
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