u(x,t0) at t0=0.00 seconds. Press any key to start the animation From the video String. mp4 from the course files, answer the following questions. The function u is u(x,t)=cos(t)sin(2x) for 0x1 and t0, where x is the spatial variable and t represents time. a) What are u(x,0) and ut(x,0) equal to for 0x1 ? These are the initial conditions. What do these represent? b) What are u(0,t) and u(1,t) equal to for t0 ? These are the boundary conditions. What is the interpretation of these? c) Show that t22u(x,t)=c2x22u(x,t) for c=21. This is the partial differential equation satisfied by u, called Wave equation. The velocity is c=21. d) For fixed 00, what do the quantities u(x0,t0),xu(x0,t0) and tu(x0,t0) represent