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.
ChickenTarm
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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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