The circular disk of mass m and moment of inertia I about its central axis is welded to...

The circular disk of mass m and moment of inertia I about its central axis is welded to the steel shaft which, in turn, is welded to the fixed block. The disk is given an angular displacement and then released, causing a torsional vibration of the disk with θ changing between The shaft resists the twist with a moment where J is the polar moment of inertia of the cross section of the shaft about the rotation axis, G is the shear modulus of elasticity of the shaft (resistance to shear stress), θ is the angle of twist in radians, and L is the length of the twisted shaft. Derive the expression for the natural frequency of the torsional vibration.