2. A uniform elastic string is stretched between the fixed points x = 0, x = 1 and its transverse dis- placement from th

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2 A Uniform Elastic String Is Stretched Between The Fixed Points X 0 X 1 And Its Transverse Dis Placement From Th 1 (40.92 KiB) Viewed 142 times

2. A uniform elastic string is stretched between the fixed points x = 0, x = 1 and its transverse dis- placement from the equilibrium position is denoted by y(x, t). The motion of the string is governed by a modified wave equation a²y 2² y ду +21= Ət² Ət əx²¹ where c> 0 and 0 << c/l are positive constants. Using the method of separation of variables, show that a solution exists in the form y(x, t) = et An sin ¹ (17²) cos (wnt + n), n=1 where the constants wn are to be found in terms of n, c, 1, X; the constants An and n are arbitrary.