The elements of analytic mechanics; Solids & fluids - Softcover

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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. 1876 Excerpt: ...same in both cases. If it slide down a smooth plane of the same slope, we have / 2« g sin t which is less than.either of the two preceding times. THE PENDULUM. X 19. Let a body be suspended on a horizon tal axis and moved by the force of gravity; required the circumstances of motion. We have d26 _ moment of forces dt moment of inertia _ TFAsintf Pio. US M¥' in which h--Oa, the distance from the axis of suspension to the centre of gravity a of the body; TP = the weight of the body; 6 = bOa; and let l = the principal radius of gyration; then the preceding equation becomes d20 gh. a df=WTBm6 This equation cannot be completely integrated in finite terms, but by developing sin 0 and neglecting all powers above the first, we find for a complete oscillation (161) which gives the time in seconds when h, kx and g are given in feet. To find the length of a simple pendulum which will vibrato in the same time, we make equations (5), page 196, and (161) equal to one another, and have l = +A = Od. (162) Let ad = then lh = K = ki;.: hht = if (163) 136. Definitions. A body of any form oscillating about a fixed axis is called a compound pendulum. A material particle suspended from a string without weight, oscillating about a fixed axis, is called a simple pendulum. The point d is called the centre of oscillation. It is the point at which, if a particle be placed and suspended from the axis O by a string without weight, it will oscillate in the same time as the body Od. Or, it is the point at which, if the entire mass be concentrated, it will oscillate about the axis in the same time as when it is distributed. The point O, where the axis pierces the plane xy, is called the centre of suspension. 137. Results. The centres of oscillation and of percussion coincide. (S...