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Unformatted text preview: ACM 95/100c Problem Set 5 27th April 2006 Due by 5:00PM on 5/5/2006 Please deposit all problem sets in the slot in 303 Firestone Please remember to include your section number and section instructor Each problem is worth 10 points  each part of a multipart problem is weighted equally Problem 1 (No collaboration) Consider the wave equation for a vibrating rectangular mem brane ( < x < L , < y < H ): ∂ 2 u ∂t 2 = c 2 ∂ 2 u ∂x 2 + ∂ 2 u ∂y 2 subject to the initial conditions u ( x, y, 0) = f ( x, y ) . ∂u ∂t ( x, y, 0) = g ( x, y ) Solve the initial value problem if (a) u (0 , y, t ) = 0 , u ( L, y, t ) = 0 , u y ( x, , t ) = 0 u y ( x, H, t ) = 0 (b) u x (0 , y, t ) = 0 , u x ( L, y, t ) = 0 , u y ( x, , t ) = 0 u y ( x, H, t ) = 0 Problem 2 (No collaboration) Consider the eigenvalue problem ∇ 2 φ + λφ = 0 with boundary conditions φ x (0 , y ) = 0 φ ( x, 0) = 0 φ x ( L, y ) = 0 φ ( x, H ) = 0 (a) Show that there is a doubly in nite set of eigenvalues 1 (b) If L...
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This note was uploaded on 01/08/2011 for the course ACM 95c taught by Professor Nilesa.pierce during the Spring '09 term at Caltech.
 Spring '09
 NilesA.Pierce

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