Please answer in detail with every step. Thank You.

6-1! (a) Find the total energy of vibration of a string of length L, xed at both ends, oscillating in its nth characteristic mode with an amplitude A. The tension in the string is T and its total mass is M. (Hint: Consider the integrated kinetic energy at the instant when the string is straight so that it has no stored potential energy over and above what it would have when not vibrating at all.) (b) Calculate the total energy of vibration of the same string if it is vibrating in the following superposition of normal modes: - 7x . 313' '- J'(x. t) A1 sun (-13) cos on: + .43 sm (T) cos (0,3; .. 3) (You should be able to verify that it is the sum of the energies of the two modes taken separately.)