Question

lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x ±ct) (use appropriate value of c) is the solution then g(x,t) = f(x ± ct)-f(-x ± ct) is also a solution. Show that g(0, )-0 Now use (a) and (b) to find the solution u(x,t) for the 1-D wave equation (c) lu for 0 x 00 with the initial conditions as in (a) (but for 0 x 00 ) and the Qx2 25 ot2 boundary condition u(0, 1-0. This problem describes the motion of the infinitely long elastic string fixed at a wall at one end Draw the solution to (c) on two separate graphs for t-2(di +15)/5 and (d) t-(di +15)/5 carefully noting position and height of the wave shape

d1=8

d2=9

Answer 1

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