Q8: The transverse oscillations of a stretched string of length L which is immersed in a au 1 (a’u viscous resistive flu

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Q8 The Transverse Oscillations Of A Stretched String Of Length L Which Is Immersed In A Au 1 A U Viscous Resistive Flu 1 (120.8 KiB) Viewed 28 times

Q8: The transverse oscillations of a stretched string of length L which is immersed in a au 1 (a’u viscous resistive fluid are given by the damped wave equation əx? <3 @t? = ди +a at = = For 0 < x <L, 0 <t<oo, where a < 2nc/L; with boundary and initial conditions u(0, t) 0, u(L, t) = 0, u(x, 0) = 0, ut(x, 0) = v(x), where v(x) is an initial velocity given to the string. A. Show that the solution to this problem can be expressed in the form плс ? u(x,t) = { 1, sin -Ź4, (Faim Kastila) плх L e sin t L 4 n=1 where the coefficients An satisfy: плс a ΣΑ, , 34 Korte sind nurse ) )- nix L =v(x) L 1 4 B. Assume now that: a =10, v(x)= x(x - 21) L = 21, C=100, find the exact : ) c solution in terms of x and t and compute 4, .