Consider a 1D elastic string fastened at its ends on the x-axis at x=0 and x=L and oscillating in the vertical x−y-plane. Take into account the gravity force with constant acceleration g. Assume that the linear density sigma and tension tau are constant. Formulate, using the lecture materials, the PDE problem for the two initial conditions (there is no need to derive the equation from the first principles):

a) The initial displacement is f(x), the initial velocity is 0 . 

b) The initial displacement is 0 , the initial velocity is g(x).