Calculating frequency for small torsional oscillation

[lzh]

Homework Statement

A thin, uniform, rigid disk of mass M, radius R is welded to a light, elastic shaft of radius r, length L, shear modulus G. Phi is the torsional oscillation.
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Homework Equations

Phi=TL/GI
I=pi/2*r^4(polar area moment of inertia)

The Attempt at a Solution

Since the shaft is "light", I assumed it to be massless and considered it a spring instead. I'm not sure if this is the right train of thought. I'm trying the Newtonian approach of equating torque:

I(total)*phi"=torque of shaft+torque of disk

somehow though, I couldn't figure out the torque of the disk. If the shaft is a spring, it's torque would be k*phi.

Am I even on the right track here? Should I do conservation of energy instead?

 

[tiny-tim]

hi lzhlzh1

A thin, uniform, rigid disk of mass M, radius R is welded to a light, elastic shaft of radius r, length L, shear modulus G …

do you know what shear modulus is?

if so, write an equation for it ​

 

[lzh]

it's the ratio of shear stress to shear strain.

G=(F/A)/tan(theta)
but truthfully I don't understand what role G plays in this question except for in the phi equation i posted

 

[tiny-tim]

you'll need to use conservation of energy (ie kinetic energy of the disc plus torsional potential energy of the shaft)

but i don't know how the shear modulus in the question is related to the torsional modulus