Getaran Selaput Melingkar pada Persamaan Gelombang Dua Dimensi dalam Koordinat Polar

Abstract

A first, we used our knowledge of Fourier series to solve several interesting boundary value problems by the method of separation of variables. The success of our method depended to a large extent on the fact that the domains under consideration were easily described in Cartesian coordinates. In this paper/research we address problems where the domains are easly described in polar and cylindrical coordinates. Spesifically we consider boundary value problems for the wave, heat, Laplace and Poisson equation over disks or cylinders. Upon restating these problems in suitable coordinat systems and separating variables, we will encounter new ordinary differential equations, Bessel’s equation, whose solutions are called Bessel function in ways analogous to Fourier series expansions. The vibrations of  the membrane are governed by the two-dimensional wave equation, which will be expressed in polar coordinantes, because these are the coordinates best suited to this problem. Finally, we will solve the two dimensional wave equation in polar coordinates (general case).