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Hi guys, I have been trying to find the "floppy" resonant mode frequency of a simple oscillator. The displacement is in the order of nanometers, while the dimensions of the oscillator is in cm. I think small angle approximations apply here. I got to the point of the equation of motion, but I have no idea how to solve it.

The equation for the shear modulus is defined. I used it to find the force.

I related force to torque.

I used maclaurin's expansion on cos θ and tan θ to approximate the equation in terms of θ.

Would appreciate any help.

The equation for the shear modulus is defined. I used it to find the force.

I related force to torque.

I used maclaurin's expansion on cos θ and tan θ to approximate the equation in terms of θ.

Would appreciate any help.

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