Two identical simple pendulums each of length L are connected by a weightless spring as shown in figure. The force constant of the spring is k. In equilibrium, the pendulums are vertical and the spring is horizontal and un-deformed. Find the time of small oscillations of the linked pendulums, when they are deflected from their equilibrium positions through equal displacements in the same vertical plane
(a) in the same direction,
(b) in opposite direction and released.