Solve the following:

' Let u E 02(R3 x [0,1]) be such a solution of the onedimensional wave equation fu, 1E) 831473, m) = 0 for which u(t,0) = u(t,l) = 0 for every t > 0 (this is a rod with xed ends). Show that then in this case the following function (mechanical energy) does not depend on t: E(t) = g [0 [(8tu(t,:1:))2+(8mu(t,:c))2]dzn