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(Solved): Figure 1 below shows the initial position function f(x) for a stretched string (of length L ) that ...
Figure 1 below shows the initial position function f(x) for a stretched string (of length L ) that is set in motion by moving its midpoint x=2L? aside the distance 21?bL and then releasing it from rest at time t=0. The corresponding boundary value problem is Utt?=a2Uxx?(0<x<L,t>0)U(0,t)=U(L,t)=0,U(x,0)=f(x)Ut?(x,0)=0? where f(x)=bx for 0?x?L/2 and f(x)=b(L?x) for 2L??x?L. Find U(x,t) Figure 1: Stretched string [20 Marks]
To solve the given boundary value problem, we will use the method of separation of variables. We assume that the solution can be represented as a product of two functions, one depending only on x and the other depending only on t:
Substituting t...