Calculus, with applications; an introduction to the mathematical treatment of science (1900)
Hayes, Ellen, 1851- · Boston, Allyn and Bacon · leaf 93
taching the ball to theend of a string whose otherend is fastened at the cen-ter of the circle. We nowhave a pendulum. Let Cbe the center of the circle;Fig. 7. 0 its lowest point; OX the #-axis, and OY the y-axis.Let A be the starting point of the ball; then at A t = 0and vQ = 0. Let P be its… … SIMPLE PENDULUM. 83 but (*Y-Pf^ \dtj \dt. hence [ —-) = -3- (cos 0 — cos a) 4gf . 2a -off= —^ smz snr - I \ 2 2 and therefore — = - 2\k Jsin2 - - sin2 £dt * l* 2 2 Notice that after extracting the square root only theminus sign is used, because dt is positive and d0 isnegative. We now have Vf^=- dd…
Calculus · Geometry, Analytic
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