Using equations 4 and 5 above and parsevals theorem show

Question

Question: (a) By analogy with Problem above, argue that

is the world's only candidate for the energy in a vibrating string.

(b) Using equations (4) and (5) above and Parseval's Theorem, show that the energy in the string considered above is finite provided that 1 and g are finite energy initial conditions.

(c) Show that the string energy is in fact constant, independent of time, and given by

Problem: Consider the spring-mass analogue of the wave equation with X₀ = X_M = 0 as boundary conditions. Define the total mechanical energy

And show (by differentiation, to cite one way) that E is independent of time.