# An Elementary Text-Book of Mechanics (Kinematics and Dynamics)

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## Description

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. 1885 edition. Excerpt: ...small lead ball suspended by a fine silk string may for most experiments be regarded as a simple pendulum. A Compound Pendulum is a mass of any shape oscillating round a fixed axis. 153. When the ranges are very small compared with th-? length of the pendulum, the time of a vibration does not depend on the length of the range. Galileo was the first to observe this fact, and to apply the pendulum to measure equal intervals of time. It becomes of great importance therefore to determine on what the time of vibration of a pendulum depends and we proceed to find an expression for the time of vibration of a Simple Pendulum when oscillating in small arcs. 154. To find the time of vibration of a simple pendulum. Let A be a material particle suspended from O by a string OA, supposed to be without weight, and let it oscillate in an arc BB' so small that the arcs BA, CA may be regarded as coinciding with their chords. Let OA = J, BA = a, CA = x. At any point C let the velocity be called v, and at A be V; then (Art. 152) the velocity at B is zero; the velocity v at C = V27-DE = / (a2-ond the velocity V at A. = VZg.J)A = a f% Let BCAB' be a straight line equal to the arc BB', and let a particle oscillate on this straight line with the same velocities as the pendulum on the arc BB'. Each will therefore start from the point B with the velocity o, will have a velocity oat C and a velocity V at A, and equal velocities at the corresponding points of their paths. Upon BB' describe a semicircle BMLB', and let another particle move along this semicircular path with the uniform "V i time taken by this latter particle to describe the semicircumference will be the same as that taken by the former to describe the straight line BB'. For the horizontal...show more

## Product details

• Paperback | 66 pages
• 189 x 246 x 4mm | 136g
• Miami Fl, United States
• English
• black & white illustrations
• 1236527399
• 9781236527394