Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 1 - 10 of 10 on We may readily prove from this that in order to deduce the motion depending on initial....
" We may readily prove from this that in order 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... "
The Theory of Sound - Page 129
by John William Strutt Baron Rayleigh - 1894 - 984 pages
Full view - About this book

The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1877 - 984 pages
...velocity, but with a displacement of the corresponding type. We may readily prove from this that in order to deduce the motion depending on initial displacements...the corresponding initial displacements. Thus, if <f> be any normal co-ordinate satisfying the equation the solution in terms of the initial values of...
Full view - About this book

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...
Full view - About this book

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,...
Full view - About this book

Mathematical and Physical Papers, Volume 2

Sir George Gabriel Stokes, Sir Joseph Larmor, John William Strutt Baron Rayleigh - 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,...
Full view - About this book

The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1894 - 984 pages
...velocity, but with a displacement of the corresponding type. We may readily prove from this that in order to deduce the motion depending on initial displacements...equation the solution in terms of the initial values of <f> and < is <f, = <f>, cos nt + - 4,, sin nt ..................... ( 1 ), ?t of which the first...
Full view - About this book

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...
Full view - About this book

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...
Full view - About this book

The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh, Robert Bruce Lindsay - Science - 1945 - 520 pages
...prove from this that in order ' Dynamical Theory of Dijfroctton, Camhridn? Trani. VoL ix. p. 1. 1866. to deduce the motion depending on initial displacements...initial displacements. Thus, if < be any normal co-orjiinate satisfying the equation $ + n*$ = 0, the solution in terms of the initial values of <j,...
Limited preview - About this book

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...
Full view - About this book

Proceedings of the Cambridge Philosophical Society ..., Volumes 1-2

Science - 1863
...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...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download PDF