# Homework Help: How do I find the normal modes of massless string w/ masses?

1. Oct 25, 2015

### ChickenTarm

1. The problem statement, all variables and given/known data
So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1
http://www.physics.purdue.edu/~jones105/phys42200_Spring2013/Assignment_5_Spring2013.pdf

2. Relevant equations
ν * λ = velocity
velocity = sqrt(T * L / M)
νn = nν1 n = 1, 2, 3
ν1 = √(T/(4ML))

3. The attempt at a solution
I tried using coupled oscillators and the equation for finding the frequencies.
ωq=2ω0|sin(q/2)|
q = nπ/(N+1) where n is the index and N is the number of particles
This does not give me the correct answer.
The correct answer is: .84ν1, 1.55ν1, and 2.04ν1.

Last edited: Oct 25, 2015
2. Oct 25, 2015

### TSny

Hello. Welcome to PF!

What did you use for ωo?

3. Oct 25, 2015

### ChickenTarm

ω02 = T/((M/3)(L/4))

4. Oct 25, 2015

### TSny

OK. That should give the correct answer. You'll have to show your detailed calculations in order to find the mistake.