A "torsional pendulum" comprises a uniform vertical quartz fiber attached to the top of a uniform solid sphere of mass m = 2 kg and radius r = 0.1m. The fiber exerts a torque on the sphere that is proportional to the amount it has been twisted: torque= -k? theta, with ? = 0.7 Nm/radian. (Here the direction of the vector ?theta points parallel or antiparallel to the fiber direction.) Following the derivation of the equation of motion for a mass on a spring that we did in class, calculate the period of rotational motion of the sphere about its vertical axis. If the sphere is initially given an angular velocity of 1.5 radians/s when the fiber is relaxed, what is the angular amplitude of the subsequent motion?