Help! Coupled harmonic oscillators.

1. The problem statement, all variables and given/known data
I am working on my lab, in which I have to find eigenvalues of coupled harmonic oscillators running a) in the same direction and b) in opposite directions. Two masses, three springs.


I have to compare my calculated values to measured values. My three trials for the same-direction oscillation came back with an average frequency of 0.901 Hz. Each of the carts have mass M, 0.25 kg. I calculated the outer springs as having values of k of 35.28 Nm each, and the center spring as having a constant of 80.18 Nm.

I'm having a lot of trouble getting my measured and calculated frequencies to the same order of magnitude, let alone the same number.

I'm assuming w1 and w2 (the frequencies of each cart) should be the same, right?

2. Relevant equations


3. The attempt at a solution

Calculated frequency: 0.918 +/- 0.051 Hz (three trial average)

Assuming k=35.28 for the outer springs and the mass of each cart is 0.25 kg:

w = (35.28)/(0.25), except for it's not.

I really have a poor understanding of this, and I need help. I really appreciate it.

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