Semi- Infinite String: consider the following wave equation describing the semi-infinite vibrating string problem Pu х> 0, t > 0, dx2' u(х, 0) %3D F(x), x > 0 ди (x,0) = g(x), dt x > 0 ди (0, t) = 0,...

Extracted text: Semi- Infinite String: consider the following wave equation describing the semi-infinite vibrating string problem Pu х> 0, t > 0, dx2' u(х, 0) %3D F(x), x > 0 ди (x,0) = g(x), dt x > 0 ди (0, t) = 0, dx t > 0 %3D a) Find the d'Alembert's solution to the initial/boundary value problem. [Assuming that u is continuous at x = 0, t = = 0.] b) Show that the solution found in part (a) maybe obtained by extending the initial position and velocity as even functions (around x = : ).