(1 point) Solve the wave equation with fixed endpoints and the given initial displacement and velocity. a2 ,0<x<L, t > 0 a(0. t) = 0, u(L, t) = 0, t > 0 Ou Ot ηπα t) + B,, sin (m Now we can solve the PDE using the series solution u(r,t)-> An C computed many times: An example: t) ) sin (-1 ). The coefficients .An and i, are Fourier coefficients we have , cos n-1 sin(n pix/ L) dr | 2/L * (-Linpi)) "cos(n*pi. = L/2 |-2/(n*pi)*(-1)An + 2/(n"pi). = x(L-x)sinin pi x/L) a"n"pi 0 (1 point) Solve the wave equation with fixed endpoints and the given initial displacement and velocity. a2 ,0 0 Ou Ot ηπα t) + B,, sin (m Now we can solve the PDE using the series solution u(r,t)-> An C computed many times: An example: t) ) sin (-1 ). The coefficients .An and i, are Fourier coefficients we have , cos n-1 sin(n pix/ L) dr | 2/L * (-Linpi)) "cos(n*pi. = L/2 |-2/(n*pi)*(-1)An + 2/(n"pi). = x(L-x)sinin pi x/L) a"n"pi 0