Please answer all the questions. Thanks!

Question 1: (1 + 1 + 3 = 5 Points) Suppose I have a rope, tied at one end, and I give it a single flick so that it forms a perfect sine wave 2 metres in width, after which I hold my end at the same height as the tied end, and let the wave propagate though the rope (in other words, I watch the rope wobble). 0.5 OF (0,0) (2,0) -0.5 -1 0 0.5 1.5 2 FIGURE 1. The rope's starting configuration We will see how how the wave propagates through the rope (i.e., solve the wave equation for this rope). . The starting time t = 0 is when the rope forms the perfect sine wave (see fig. 1). . Assume for these calculations that the initial derivative w.r.t. time is zero. That is: us (x, 0) = 0.* (a) (1 Point) What are the boundary conditions for the wave equation describing this rope configuration? (b) (1 Point) What are the initial conditions for the wave equation describing this rope configuration? (c) (3 Points) Solve the wave equation for this rope configuration (i.e., find u(x, t)). Show all working