Total Energy of Vibration

  • Thread starter JB91
  • Start date
  • #1
3
0

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 enery 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 [Broken]
https://ca.answers.yahoo.com/question/index?qid=20141120113815AANH7NE [Broken]

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]
 
Last edited by a moderator:

Answers and Replies

  • #2
3
0
Oh sorry forgot to mention I figured out A, I'm only trying to solve part b now!
 

Related Threads on Total Energy of Vibration

  • Last Post
Replies
1
Views
270
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
578
  • Last Post
Replies
0
Views
962
  • Last Post
Replies
14
Views
4K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
5
Views
5K
  • Last Post
Replies
5
Views
23K
Top