HW6_10 - Given the triangular displacement initial...

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ME 563 HOMEWORK # 6 Fall 2010 PROBLEM 1: Assume that there is viscous damping distributed along a string as it vibrates. The damping coefficient per unit length is c. The density of the string is ρ , the tension is T, and the length is L. Derive the form of the transverse displacement free response, u(x,t), of the string assuming the string is fixed at both ends. PROBLEM 2: Assume a solution of the form found in Problem #1 with c=0.
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Unformatted text preview: Given the triangular displacement initial condition shown below with zero initial velocity, compute the free response along the string. Plot the solution using Matlab at t=0 using 2, 3, 10, and 20 modes of vibration to determine the accuracy of the response. Assume U=5 mm, L=1 m, and c=1000 m/s. Initial displacement L U...
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