An engineer has an odd-shaped 11.4 kg object and needs to find its rotational inertia about an axis through its center of mass. The object is supported on a wire stretched along the desired axis. The wire has a torsion constant κ = 0.428 N·m. If this torsion pendulum oscillates through 23 cycles in 45.9 s, what is the rotational inertia of the object

Question

An engineer has an odd-shaped 11.4 kg object and needs to find its rotational inertia about an axis through its center of mass. The object is supported on a wire stretched along the desired axis. The wire has a torsion constant κ = 0.428 N·m. If this torsion pendulum oscillates through 23 cycles in 45.9 s, what is the rotational inertia of the object
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I thought you could get Icm of the object through T=2pi x sqrt(Icm/K).  Solving for Icm with (T/2pi)^2 x k = Icm 
That however does not work.  I really don't know what to do about it.  Thanks in advance.

Brent · Answer

I figured out what I was doing wrong. 23cycles in 45.9s give the frequency. Not the period. I was using the frequency as T.