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Rotational Oscillations

Q- Two disks with moments of inertia I1 (top disk) and I2 (bottom disk) are connected by a mass-less torsion spring which produces a restoring torque with magnitude |τ| =  c |θ12| on each disk, where θ1 and θ2 are the angular positions of the disks. (You can imagine that this system is free floating in space subject to no other forces). The disks are  held initially at rest with the bottom disk twisted by an angle θ22I with respect to equilibrium. The top disk is held initially at θ1=0.

(a) What is the initial angular momentum? Initially, what is the total mechanical energy including kinetic energy and potential energy?

(b) The disks are then released. What is the maximum rotational kinetic energy acquired by the top disk?

(c) What is the oscillation frequency n of this system?


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