# Wave Equation String BVP

by jc2009
Tags: equation, string, wave
 P: 14 Write the BVP for the small vertical vibrations of a homogeneous string. Assume that the wave's speed is c. Problem: take L = 2[Pi] , c= 2, SUppose that the right end is fixed while the left end is allowed to move vertically. At the left end, the tangent line at any time t is horizontal. Suppose that the string is set into motion from rest with an initial position given by the function f(x) = sin3x Write the BVP Solution: u(x,0) = sin3x $$u_{t}(x,0) = 0$$ u(2[pi], t) = 0 u(0,t) = f(x) since the left end is allowed to move vertically ( is this right? )

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