Torque in cylinders - show the cylinder undergoes harmonic motion

[Maybe_Memorie]

Homework Statement

A cylinder of radius R and mass m is suspended using stainless steel
wires attached to fixed supports, so that it can rotate about its axis.
When the cylinder is rotated by an angle a the wires exert a torque
which tends to bring it back to the equilibrium position at a = 0. The
torque exerted by the wires is proportional to a,
 t=-ac
where c > 0 is a constant.

Show that the cylinder undergoes harmonic motion and compute
the associated period.

Homework Equations

The Attempt at a Solution

To be honest I've no idea where to start. I just need a hint to point me in the right direction.

Thanks!

 

[SammyS]

What is the moment of inertial of a solid cylinder, about its axis.

How are torque, moment of inertia, and angular acceleration related?