A uniform circular cylinder of mass M and radius a is free to turn about its axis which is horizontal. A thin uniform cylindrical shell of mass M/2 and radius a is fitted over the cylinder. At time t = 0 the angular velocity of the cylinder is 2, while the shell is at rest. The shell exerts a frictional torque on the cylinder of magnitude k(-), where w(t) and (t) are the angular velocities of the cylinder and shell respectively at time t about the axis. Prove that

w(t) =1/2Ω (1+e⁻4kt/Ma²)

and find the corresponding expression for w(t).