Question

(a) Consider an elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial postion J2/4 0<x<8 u(x,0) = { 0 8 << 10 Assuming the string is elastic enough to assume this initial configuration, i. Find the Fourier sine series for f (extended as an odd periodic function of period 20). ii. Assuming the propagation speed a = 2 solve the wave equation to find the displacement function u(, t).

Answer 1

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Cne m Then We + Uiny Usiny Fr Nn-Trid saludion Lt, o Sin 10 o TT hm slutin Hence, we get, The (7) There luer Let Se 00E () Nav Fr T T(t)= +dn Sin at T (t)

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