A small sphere of mass m suspended by a thread is first taken aside so that the thread forms the right angle with the vertical and then released. Find: (a) The total acceleration of the sphere and the thread tension as a function of θ, the angle of deflection of the thread from the vertical; (b) The thread tension at the moment when the vertical component of the sphere's velocity is maximum; (c) The angle θ between the thread and the vertical at the moment when the total acceleration vector of the sphere is directed horizontally