. A manual of marine engineering: comprising the design, construction, and working of marine machinery. of the moving parts only, acting on the engine as a whole and recurringevery revolution. As these are the forces that tend to make the foundation vibrate, thebalancing of an engine consists of counteracting the forces so that themoving parts are really made as if weightless when considered dynamicallyin certain given directions. It has also been stated above that the problem of balancing has nodirect relation to the speed of the engine. This will be obvious on con-sideration, for any counter
. A manual of marine engineering: comprising the design, construction, and working of marine machinery. of the moving parts only, acting on the engine as a whole and recurringevery revolution. As these are the forces that tend to make the foundation vibrate, thebalancing of an engine consists of counteracting the forces so that themoving parts are really made as if weightless when considered dynamicallyin certain given directions. It has also been stated above that the problem of balancing has nodirect relation to the speed of the engine. This will be obvious on con-sideration, for any counteracting weights that may be applied mustnecessarily have their velocity imparted to them by the engine itself, andthe factor of velocity is consequently eliminated from both sides of therepresentative equations. 2. Harmonic Motion.—The theorem of harmonic motion is stated herebecause of its great importance and the direct bearing it has on the presentsubject. Suppose a point P (fig. 205) to move uniformly round the circle X YX^.Draw two rectangular axes 0 X, 0 Y, and P N perpendicular to O Y. Then. if P has a uniform angular velocity N will move along Y 0 Y^, with a motionthat is called Simple Harmonic Motion. Let OP = r, POY=^, then O N = r cos 9. Let V = linear velocity of P, then Velocity of N = -v sin 6 v^ and Acceleration of N = cos 6. r The proof of these will be found in most treatises on theoretical mechanics. P is called the generating point. The angle & is called the phase. r is called the amplitude. The time of one revolution of P is called the period. HARMONIC MOTIONS. 645 A curve of the displacement of N from O or of the acceleration of N maybe drawn if the abscissae be made proportional to 6 and the ordinates pro- 7^uUa/nt x6o^O-^y^ ZO
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