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" PROPERTY. 129 to deduce the motion depending on initial displacements from that depending on the initial velocities, it is only necessary to differentiate with respect to the time, and to replace the arbitrary constants (or functions) which express the... "
The Theory of Sound - Page 123
by John William Strutt Baron Rayleigh - 1894 - 984 pages
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The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1877 - 984 pages
...therefore from which the conjugate property follows, if the motions represented respectively by ur and ut have different periods. A good example of the connection...the corresponding initial displacements. Thus, if <f> be any normal co-ordinate satisfying the equation the solution in terms of the initial values of...
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The theory of sound, Volume 1

John William Strutt (3rd baron Rayleigh.) - 1877
...initial displacements from that depending on the initial velocities, it is only necessary todifferentiate with respect to the time, and to replace the arbitrary...functions) which express the initial velocities by those whichi express the corresponding initial displacements. Thus, if <f> be any normal co-ordinate satisfying...
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mathematical and physical papers

1883
...we have only to differentiate with respect to t, and to replace the arbitrary constants or arbitrary functions which express the initial velocities by...which express the corresponding initial displacements. Conversely, to get the disturbance due to the initial velocities from that due to the initial displacements,...
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Mathematical and Physical Papers, Volume 2

George Gabriel Stokes - Hydrodynamics - 1883
...we have only to differentiate with respect to t, and to replace the arbitrary constants or arbitrary functions which express the initial velocities by...which express the corresponding initial displacements. Conversely, to get the disturbance due to the initial velocities from that due to the initial displacements,...
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The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1894 - 984 pages
...Dynamical Theory of Diji ruction, Cambridge Trans. Vol. IX. p. 1, 1856. 95.] CONJUGATE PROPERTY. 129 to deduce the motion depending on initial displacements...equation the solution in terms of the initial values of < and < is <f> = <0cos nt + -<f>0smnt ..................... (1), ?1 of which the first term may...
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The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1894
...Dynamical Theory of Diffraction, Cambridge Tram. Vol. ix. p. 1, 1856. 95.] CONJUGATE PROPERTY. 129 to deduce the motion depending on initial displacements...equation the solution in terms of the initial values of < and < is <f> = <„ cos nt + - <0 sin nt ..................... (1), of which the first term...
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Mathematical and physical papers, Volume 5

George Gabriel Stokes - Mathematics - 1905
...which depends upon the initial velocities by replacing the arbitrary functions, or arbitrary constants, which express the initial velocities by those which express the corresponding initial displacements, and differentiating with respect to the time." One of the principal objects of the memoir was to determine...
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Proceedings of the Royal Society of London, Volume 75

Electronic journals - 1905
...which depends upon the initial velocities by replacing the arbitrary functions, or arbitrary constants, which express the initial velocities by those which express the corresponding initial displacements, and differentiating with respect to the time." One of the principal objects of the memoir was to determine...
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Philosophical Magazine

Science - 1850
...differentiating with respect to the time, and replacing the arbitrary functions, or arbitrary constants, which express the initial velocities by those which express the corresponding initial displacements. Particular cases of this theorem are of frequent occurrence, but the author is not aware of any writing...
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mathematical and physical papers

...which depends upon the initial velocities by replacing the arbitrary functions, or arbitrary constants, which express the initial velocities by those which express the corresponding initial displacements, and differentiating with respect to the time." One of the principal objects of the memoir was to determine...
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