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transmission of vibrations vibration of a building vibration of a string torsional
the telegraphic equation partial difference equations simultaneous equations
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aerofoil analytic angle approximation arbitrary constants arbitrary function axis boundary conditions bounded centre co-ordinates coefficients components consider continuous continuous function converges corresponding cosh cylinder denote density derived dx dy electric elliptic equations of motion equipotential equipotential curve expansion expression finite flow fluid force formula Fourier series function F generalised given Green's function Green's theorem heat Hence inequality infinite interval Laplace's equation linear London Math mapping method obtained orthogonal oscillations partial differential equation plane Poisson's polynomial potential function primary solutions Proc Prove quadratic form quantity radius regarded region relation represented respectively result satisfied simple sin2 sinh solution of Laplace's solution of type sphere supposed surface integral theorem theory transformation uniformly unit circle variables vector velocity velocity potential vertical vibration W. H. Young wave-equation wave-function waves write z-plane zero