11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a ring that is free to slide up and down a vertical pole. One can show that under these assumptions the tangent line to the free end will always be horizontal. Separate variables and describe the motion of the string at any time t> 0, given any initial shape and (vertical) velocity. Positioning the string along the interval [0, L] of the x-axis, solve the boundary value problem by separation of variables. Utt = c²uxx, 0 < x 0 ur(0,t) = u(L,t)=0, t>0 u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L

11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a ring that is free to slide up and down a vertical pole. One can show that under these assumptions the tangent line to the free end will always be horizontal. Separate variables and describe the motion of the string at any time t> 0, given any initial shape and (vertical) velocity. Positioning the string along the interval [0, L] of the x-axis, solve the boundary value problem by separation of variables. Utt = c²uxx, 0 < x 0 ur(0,t) = u(L,t)=0, t>0 u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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