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Wave Equation Modeling of Vibrating String

Wave Equation Modeling of Vibrating String. The tension is tangential to the curve T 1 and T 2 are the tension at the endpoints P and Q is the mass of the string per unit length No motion in the horizontal direction The weight of the string is neglected.

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Wave Equation Modeling of Vibrating String

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  1. Wave EquationModeling of Vibrating String • The tension is tangential to the curve • T1and T2 are the tension at the endpoints P and Q • is the mass of the string per unit length • No motion in the horizontal direction • The weight of the string is neglected

  2. Wave EquationModeling of Vibrating String

  3. Wave EquationModeling of Vibrating String

  4. Modeling of Vibrating String PDE u(x,t) x x=0 x=L boundary conditions initial conditions

  5. Solution by Separating VariablesUse of Fourier Series boundary conditions initial conditions

  6. Solution by Separating VariablesUse of Fourier Series

  7. t1 t2 t3 tK Computational Aspects

  8. t1 t2 t3 tK Computational Aspects • Use FFT to compute

  9. Implementation by Matlab function a=sincof(func,hafper,nft) • Use FFT to compute u=((a(ones(length(x),1),:).*sin(x*w))*cos(w(:)*t))';

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