Torsional Vibration Theory Question - k value help

[DFC101]

Homework Statement

I've been given this as a piece of coursework and I'm having a bit of trouble starting it. I know most of what I need to do once I can figure out how to calculate a few basic (though essential) values.

The first part to the question is as follows:

"Determine, using matrix methods involving the Dynamic Characteristic Matrix Equation {DM}, and hand calculations, the natural frequencies of torsional vibration ignoring the effect of IC (coupling) mass inertia effects for the model indicated in figure 2 but including all stiffness elements."

Homework Equations

None supplied in this coursework however here are the relavent formulae for this section of the module I am studying:

The Attempt at a Solution

I'm not entirely sure how to enter equations on this forums so I've just provided a print screen of my working so far...

Any help would be greatly appreciated. I Imagine the answer is fairly obvious however vibration theory has always been one of my weak points!

Cheers, DFC

 

[rock.freak667]

I think J would be the inertia of the entire system, not just the shaft alone. They gave you radii of gyration as well as the inertia of the gearbox and couplings.

However using that equation will give you the equivalent torsional stiffness. I am just not sure if torsional springs in series act similarly to linear springs in series though.