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In the article: "Beam to String Transition of Vibrating Carbon Nanotubes Under Axial Tension" I have found an equation that describes the resonance frequency of a beam under axial tension.

However, I have some problem solving it.

The equation looks like this:

x + y*Sinh[y + Sqrt[y^2 + x^2]]^0.5*Sin[-y + Sqrt[y^2 + x^2]]^0.5 -

x*Cosh[y + Sqrt[y^2 + x^2]]^0.5*Cos[-y + Sqrt[y^2 + x^2]]^0.5 = 0

x is the dimensionless natural frequency and y is the dimensionless natural frequency parameter.

I want to find the x for different y.

I have tried to solve this equation i Mathematica but without much success.

Can anyone help me?

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# How do I solve this equation?

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