2. The model of a vibrating elastic string consists of the one-dimesional wave equation is written...

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2. The model of a vibrating elastic string consists of the one-dimesional wave equation is written as 2²u at² ₂0²u əx²* Using the separation of variable method and the boundary conditions u(0, t) = u(L, T) = 0, the solution of the wave equation can be written as u(x, t) = [ ¹₁(x, t) = [ (B₂, cos Ant + Bi; sin λt) sin ( n=1 It is given that the string of length L = 1 and c² = 1. n (7x). Now find the constants Band B by using the Fourier series when the initial velocity is zero and the initial deflection u(x, 0) with small k(say = 0.01) is as follows. (2x - 4x², 0, 0<x< 1/2 1/2<x< 1 [20] 2. The model of a vibrating elastic string consists of the one-dimesional wave equation is written as 2²u at² ₂0²u əx²* Using the separation of variable method and the boundary conditions u(0, t) = u(L, T) = 0, the solution of the wave equation can be written as u(x, t) = [ ¹₁(x, t) = [ (B₂, cos Ant + Bi; sin λt) sin ( n=1 It is given that the string of length L = 1 and c² = 1. n (7x). Now find the constants Band B by using the Fourier series when the initial velocity is zero and the initial deflection u(x, 0) with small k(say = 0.01) is as follows. (2x - 4x², 0, 0<x< 1/2 1/2<x< 1 [20]

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Vibrating Elastic String Solution To find the constants Bn and Bn in the solution of the wave equati... View the full answer