A rectangular membrane with its corners at (0,0). (a,0). (a, b), and (0, b) has its...

 

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A rectangular membrane with its corners at (0,0). (a,0). (a, b), and (0, b) has its edges clamped. The governing equation is the two-dimensional wave equation in Cartesian coordinates 8²u 01² Pu 0x² Oy² (1) where e is the wavespeed, and u(x, y, t) is the vibrational amplitude. Show that the natural vibrational frequencies (related to the eigenvalues Amn) are given by H 20 7676 Wmn ="V (F) and that the corresponding eigenfunctions determining the modes of vibration Omn (1, y) = sin 36 NTI SHIL 2 A rectangular membrane with its corners at (0,0). (a,0). (a, b), and (0, b) has its edges clamped. The governing equation is the two-dimensional wave equation in Cartesian coordinates 8²u 01² Pu 0x² Oy² (1) where e is the wavespeed, and u(x, y, t) is the vibrational amplitude. Show that the natural vibrational frequencies (related to the eigenvalues Amn) are given by H 20 7676 Wmn ="V (F) and that the corresponding eigenfunctions determining the modes of vibration Omn (1, y) = sin 36 NTI SHIL 2