How do I find the normal modes of massless string w/ masses?

AI Thread Summary
To find the normal modes of a massless string with three equally spaced masses, the tension T and length L are crucial for calculating the frequencies of transverse motion. The velocity of the wave is determined by the formula sqrt(T * L / M), and the fundamental frequency is given by ν1 = √(T/(4ML)). The attempt to use coupled oscillators led to incorrect results, prompting a reevaluation of the calculations. The correct frequencies for the smallest three modes are approximately 0.84ν1, 1.55ν1, and 2.04ν1. Detailed calculations are necessary to identify any mistakes in the initial approach.
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Homework Statement


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

Homework Equations


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

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:
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Hello. Welcome to PF!

What did you use for ωo?
 
TSny said:
Hello. Welcome to PF!

What did you use for ωo?
ω02 = T/((M/3)(L/4))
 
OK. That should give the correct answer. You'll have to show your detailed calculations in order to find the mistake.
 

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