Cube and Sphere Period Comparison with Same Wire and Restoring Force Constant?

[kevinf]

Homework Statement

In the experiment, you will study an oscillator called a "torsion pendulum."
In this case, the restoring "force" is the torsion constant of the wire that
suspends the weight X and the inertial term is the rotational inertia of the
suspended mass. You will compare the periods of a suspended sphere and of a
suspended cube. The rotational inertia of a sphere is Is = 1/10M_sD^2 where
ms is the mass of the sphere and D is its diameter. The rotational inertia
of a cube is Ic = 1/6m_S^2 where mc is the mass of the cube and S is the
length of its side. If the cube and the sphere are suspended from the same
wire, what is the expected ratio of their periods, Tc/Ts?
Assume that D = S
ms = 0.20kg
and mc = 0.9 kg

Homework Equations

T=1/f, omega = 2pi*f

The Attempt at a Solution

so for this one I know that I can get the moment of inertia and get the
angular frequency but I don't know what the restoring force constant k is.
is that constant require or would it cancel out later on?

 

[kevinf]

bump...

 

[turin]

First work it out symbolically.