Oscillation

“ I shall finish my discourse on pendulums, with this farther observation only, that the center of oscillation is also the center of another force. If a body be fixed to any point, and being put in motion turns round it; the body, if uninterrupted by the power of gravity or any other means, will continue perpetually to move about with the same equable motion. Now the force, with which such a body [101] moves, is all united in the point, which in relation to the power of gravity is called the center of oscillation. Let the cylinder A B C D (in fig. 60.) ”

“ After-oscillation.—In the case of the sensitive silver cell, we have seen (fig. 105) , when it has been subjected for some time to strong light, that the current of response attains a maximum, and that on the stoppage of the stimulus there is an immediate rebound towards recovery. In this rebound there may be an over-shooting of the equilibrium position, and an after-oscillation is thus produced. ”

“ In the second, or retrograde oscillation, the plane, returning through the same space, must communicate to the stratum of fluid in contact with it, and to the rest in succession, a motion in a direction contrary to that of the first oscillation; for when the plane recedes, the stratum in contact with it, urged against the plane by the elasticity or the expansive force of the fluid, necessarily follows it, and fills up the vacuum which its retrograde motion tends to produce. ”

“ Illustrations were drawn from mechanics, such as the examples furnished by vibrating pendulums and springs, and from acoustics, as illustrated by the phenomena of resonance, to show that small or feeble blows or impulses delivered at the proper time intervals have a cumulative effect in setting up vibrations in a body capable of oscillation. ”

“ But if, on the other hand, the molecules of the one mass have periods of oscillation different from those of the other mass, their mutual impacts will not agree with the period of oscillation of either, but will generate a new rhythm, differing from, and much slower than, that of either. ”

“ While an ethereal particle is performing a complete oscillation, a series of others, to which it has communicated its motion, are also performing oscillations in various phases—the adjacent particle being a little behind the first, the next a little behind the second, and so on, until, in the file of particles, we come to one which is in the same phase of its oscillation as the first one. ”

“ At the same time, however, that I assert the inefficacy of any experiments with the pendulum as tending to show the earth's rotation, I admit that, provided a pendulum could be made to preserve its plane of oscillation for twenty-four hours, it would oscillate independently of the rotation of the earth, and actually describe a circle round a fixed table in that interval. ”

“ And, since each particle of the ocean executes periodic oscillations about a mean position, it follows that the oscillation of the ocean imparts to the solid earth oscillations such that the resultant moment of momentum of the whole system remains constant. ”

“ Now it is a general law of frictionless oscillation that, if a slowly varying periodic force acts on a system which would oscillate quickly if left to itself, the maximum excursion on one side of the equilibrium position occurs simultaneously with the maximum force in the direction of the excursion; but, if a quickly varying periodic force acts on a system which would oscillate slowly if left to itself, the maximum excursion on one side of the equilibrium position occurs simultaneously with the maximum force in the direction opposite to that of the excursion. ”

“ The trajectory of Earth deviates as little from a circle, that, when we are dealing with sun rays, we can neglect the velocity component , on which the variation of the oscillation period depends (§ 37) . ”

“ The cause of the oscillations is gravity, or the attractive power of the earth. Since this force diminishes as the square of the distance from the earth's center increases, its amount at different elevations above the surface may be exactly calculated. The time required for the vibration of the pendulum is, in consequence of the same law, longer at heights above, shorter at points below the surface of the earth, than at the surface itself ”

“ In two oscillations we can see no effect on the time produced by the amplitude, and we are correct in saying that, when the amplitude is only a small fraction of the length of the pendulum, its effect is inappreciable. ”

“ The greater or less amplitude of the oscillations of the strata of the fluid determines the degree of absolute velocity with which they move, and consequently the energy, but not the nature of the sensation which they excite, which must depend, according to every analogy, upon the duration of the oscillations. It is thus that the nature of the sounds, transmitted by the air to our ears, depends entirely on the duration of each of the oscillations executed by the air, or by the sonorous [p121] body which puts it in motion ”

“ All the properties which have been explained as belonging to a simple pendulum may thus be transferred to a vibrating body of any magnitude and figure, by considering it as equivalent to a single particle of matter vibrating at its centre of oscillation. ”

“ This precise and detailed account of the Undulatory Motion of air by which sound is transmitted was first given by Newton. He further attempted to determine the motions of the separate particles, and to point out the force by which each particle affects the next, so as to continue the progress of the undulation once begun. The motions of each particle must be oscillatory; he assumed the oscillations to be governed by the simplest law of oscillation which had come under the notice of mathematicians, (that of small vibrations of a pendulum;) ”

“ Every time that the flashing light gains or loses one complete flash, upon the motion of the tuning-fork, it will appear to make one complete oscillation, and the water-drops will appear to move back or on one place. ”

“ Then I numbered the oscillations in which the globe would lose part of its motion. If the pendulum was drawn aside from the perpendicular to the distance of 2 inches, and thence let go, so that in its whole descent it described an arc of 2 inches, and in the first whole oscillation, compounded of the descent and subsequent ascent, an arc of almost 4 inches, the same in 164 oscillations lost part of its motion, so as in its last ascent to describe an arc of 13⁄4 inches. ”

“ Hence, and on account of the superposable character of the motions which we are considering, we may conclude that the values of at any given point in the medium are capable of expression as linear functions of in a manner which shall be independent of the time and of the orientation of the wave-planes and the distance of a nodal plane from the point considered, so long as the period, of oscillation remains the same. ”

“ In order to obtain some measure of the vertical oscillation of the earth, a weight might be attached to a spiral spring, or a pendulum might be sustained in a horizontal position, and a sliding index be moved by either of them, so that the extreme deviations should be indicated by it. ”

“ When these dissipative forces are disregarded, it is found that an elastic solid body is capable of vibrating in such a way that the motion of any particle is simple harmonic motion, all the particles completing their oscillations in the same period and being at any instant in the same phase, and the displacement of any selected one in any particular direction bearing a definite ratio to the displacement of an assigned one in an assigned direction. ”

“ For instance, I believe that the mass of the earth generally, and therefore, also, in an especial way, its more considerable continents, do not exercise a constant and invariable force of attraction, but that this attractive force manifests itself by a certain pulse, which, according to intrinsic, necessary, and probably, also, accidental external causes, increases or decreases. Though all attempts by other objects to determine this oscillation may be too limited and rude, the atmosphere furnishes a standard both delicate and large enough to test their silent operations. ”

“ Atoms and molecules may vibrate to and fro, or may execute various oscillations about each other, with a moderate velocity, or perform their motions with a rapidity beyond conception; and be the intensity of the vibrations ever so great or ever so small, these same vibrations determine the amplitude of the ethereal waves—those waves of greatest length giving rise to all the phenomena of radiant heat, while shorter ones constitute light in all its luminous and chromatic effects ”

“ That the oscillations of the pendulum are caused by the earth, is proved by similar evidence. Those oscillations take place between equidistant points on the two sides of a line, which, being perpendicular to the earth, varies with every variation in the earth’s position, either in space or relatively to the object. Speaking accurately, we only know by the method now characterized, that all terrestrial bodies tend to the earth, and not to some unknown fixed point lying in the same direction. ”

“ When a body is placed on a horizontal axis which does not pass through its centre of gravity, it will remain in permanent equilibrium only when the centre of gravity is immediately below the axis. If this point be placed in any other situation, the body will oscillate from side to side, until the atmospherical resistance and the friction of the axis destroy its motion. (159, 160.) Such a body is called a pendulum. The swinging motion which it receives is called oscillation or vibration. ”

“ The degree or mode of aggregation will not, indeed, affect the rate or extent of rhythm where the incident force increases as the aggregate increases, which is the case with gravitation: here the only cause of variation in rhythm, is difference of relation to the incident forces; as we see in a pendulum, which, though unaffected in its movements by a change in the weight of the bob, alters its rate of oscillation when taken to the equator. ”

“ Free fall in a vacuum, propagation of light and sound waves without absorption and reflection and unchecked electrical oscillations. All the latter processes are either naturally periodic, or they can be made completely reversible by suitable devices so that no sort of change in Nature remains behind; for example, the free fall of a body by utilizing the velocity acquired to bring the body back to its original height, light and sound waves by suitably reflecting them from perfect mirrors. ”

“ Hence from the times of the oscillations in unequal arcs in a resisting medium, may be known the times of the oscillations in a non-resisting medium of the same specific gravity. For the difference of the times will be to the excess of the time in the lesser arc above the time in a non-resisting medium, as the difference of the arcs to the lesser arc. ”

“ A complete horizontal oscillation occupies the time of two steps, and, consequently, of two vertical oscillations. The body is carried toward the right side, at the moment of the maximum of elevation, which corresponds with the middle of the pressure on the right foot, and toward the left at the middle of the pressure on the left foot. This lateral swaying of the trunk is the consequence of the alternate passage of the body into a position sensibly vertical over each foot.
The body is advancing at every moment during the step, but at some parts of it more rapidly than at others. ”

“ It is proved by daily experience, as well as by strict mechanical reasoning, that if a number of waves or oscillations be excited in a fluid by different forces, each pursues its course, and has its effect independently of the rest. ”

“ The supposition is, that there are motions which manifest themselves to our senses only as heat, electricity, etc., being molecular motions; oscillations, invisible to us, among the minute particles of bodies ”

“ It then recommences, at similar periods, the series of motions which have been described, and would continue to oscillate for ever, but for the effect of the resistance of the surrounding fluid, the inertia of which continually diminishes the amplitude of its oscillations, and finally extinguishes them at the end of a longer or shorter time, according to circumstances. ”

“ Again, so long as they are not agitated, the incident force cannot separate the heavier units from the lighter; agitate them, and immediately the heavier units begin to segregate. By these illustrations, a rude idea will be conveyed of the effect which vibration has in facilitating those re-arrangements which constitute Evolution. What here happens with visible units subject to visible oscillations, happens also with invisible units subject to invisible oscillations. ”

“ We have already seen that all motion is rhythmical, from the infinitesimal vibrations of infinitesimal molecules, up to those vast oscillations between perihelion and aphelion performed by vast celestial bodies. And as the contrast between these extreme cases suggests, a multiplication of rhythms must accompany a multiplication in the degrees and modes of aggregation, and in the relations of the aggregated masses to incident forces. ”

“ OSCILLATIONS, ELECTRIC.--A current of high frequency that surges through an open or a closed circuit. (1) Electric oscillations may be set up by a spark gap, electric arc or a vacuum tube, when they have not only a high frequency but a high potential, or voltage. (2) When electric waves impinge on an aerial wire they are transformed into electric oscillations of a frequency equal to those which emitted the waves, but since a very small amount of energy is received their potential or voltage is likewise very small. ”