Calculating Total Energy of Vibration for a String

[JB91]

Homework Statement

a.) Find the total energy of vibration of a string of length L, fixed 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 is it is vibrating in the following superposition of normal modes:
y(x,t)=A1sin( xpi/L)cos(w1t) + A3sin(3xpi/L)cos(w3t- pi/4)
(You should be able to verify that it is the sum of the energies of the two modes separately.)

Answers:
a.) (A^2)(n^2)(pi^2)T/4L
b.) (A1^2 + 9A3^2)(pi^2)(T)/4L[/B]

Homework Equations

y(x,t)=A1sin( xpi/L)cos(w1t) + A3sin(3xpi/L)cos(w3t- pi/4)
U=1/2 mu (dy/dt)^2 + T/2 (dy/dx)^2[/B]

The Attempt at a Solution

https://ca.answers.yahoo.com/question/index?qid=20141120113724AAqz07h
https://ca.answers.yahoo.com/question/index?qid=20141120113815AANH7NE

Thats my attempt, final answer is off ( i put the answer from textbook at the bottom of the last page), sorry couldn't figure out how to post . Any help would be greatly appreciated!

also i just tried to get rid of the omegas using : w(n)=npi/L (T/mu)^(1/2) where mu=M/L
[/B]

 

[JB91]

Oh sorry forgot to mention I figured out A, I'm only trying to solve part b now!