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, then 

total acceleration of sphere as a function of $\theta$ is $g\sqrt{ 1+3{\cos }^2\theta }$

thread tension as a function of $e$is$T =3mg \cos \theta$

the angle $\theta$ between the thread and the vertical at the moment when the total acceleration vector of the sphere is directed horizontally is ${\cos }^{-1} 1/\sqrt{ 3}$

the thread tension at the moment when the vertical component of the sphere's velocity is maximum will be $mg$