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The general solution y(t, p. 6) to the wave equation on a disc of radius R with boundary condition v(t, R, 1) = 0 is given by vlt,0,0) = EE - ( ) [cos (ES) (Am.cos(nb) + Bu sin(no)) + (ME) (C..cos(no) + Dm (no) n=0 s=0 sin sin(ne)) 728 where Jn (2) is a Bessel function and x is the s'th root of In(x). (i) Derive the expressions for y and Oy/at at t = 0. (ii) Find all Ans, Bns, Cns, and Drs such that ¥ (0, 0,0) = 3 cos(20)52 () and a at 410, 0, 0) = 2 sin(Q)J] (x2) Hence give the expression for v(t, p. 6) satisfying all above conditions.
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