2. Solve the string problem with a constant source term in the equation representing gravity 8²u c². g, at2 ax2 a²u u(0,t) = 0, u(L,t) = 0,u(x, 0) = f(x), du (x, -(x, 0) = 0 You can solve it by superposition principle by dividing the problem into a time independent part and another time dependent part. Show all the details what the different parts solve and how the boundary conditions are satisfied. Leave the expansion coefficients in the integral form. What does the time independent part represent? We talked about in class the following wave problems 8²u o²u 1. =c² 2 812 ди ди u(0,t)=u,(L,t) = 0, u(x, 0) = f(x),(x, 0) = 0 ax at The boundary condition at x = L is the free boundary condition. Leave the expansion coefficients in the integral form just as we did for heat equation.