I’ve been attempting to crack this drawback for some time however can’t appear to determine what to do with the Neumann Boundary Situation. The issue is to resolve the next:

start{equation*}
u_{tt}-u_{xx}=0
u(x,0) = 0
u_t(x,0)=start{instances}
pi cos(pi (x-1)), & 1<x<2
0 & else
finish{instances}
finish{equation*}

For the next
1. $$ x in (-infty, infty)$$
2. $$x in (0, infty) textual content{ and } u_x(0,t) = 0$$
3. $$x in (-infty, 3) textual content{ and } u(3,t) = 0$$

I understand how to do 1, it is merely making use of D’Alemebert system. However I’m misplaced for two and three.