A disk of radius a and mass m is suspended at its centreby a vertical torsion wire which exerts a couple -cθ on the diskwhen it is twisted through an angle θ from its equilibriumposition. Show that oscillations of the disk are simple harmonic,and obtain an expression for the period. A wire ring of mass m andradius a/2 is dropped concentrically onto the disk and sticks toit. Calculate the changes to (a) the period (b) the amplitude (c)the energy of the oscillations for the two cases where the ring isdropped on (i) at the end of the swing when the disk isinstantaneously at rest (ii) at the midpoint of the swing when thedisk is moving with its maximum angular velocity.
