Let us twist (rotate) the disc through a small clockwise angle
θ. Then, the spring will be deformed (compressed) by a distance
x=Rθ. Hence, the spring force
Fs=kx=k(Rθ) will produce a restoring torque.
Restoring torque,
τ=−FsR where
Fs=kRθ
This gives,
τ=−kR2θ .....(1)
It means that after removing the external, (applied) torque, the restoring torque rotates the disc with an angular acceleration
α which will bring the spring disc system back to its original state.
Applying Newton's second law for rotational motion, we have
τ=Iα
Using
(1) in the above formula, we get
−kR2θ=Iα
This gives
α=−kR2θI
Moment of inertia of a disc about an axis passing through its COM is given by
I=mR22
Thus,
α=−2kmθ
Comparing the above equation with
α=−ω2θ, we get
ω=√2km
From the data given in the question,
ω=√2×105⇒ω=2 rad/sec