A simple pendulum of length L has a bob of mass m. The bob is connected to light horizontal spring of force constant k. The spring is relaxed when the pendulum is vertical (see fig (i)).
(a) The bob is pulled slightly and released. Find the time period of small oscillations. Assume that the spring remains horizontal.
(b) The spring is replaced with an elastic cord of force constant k. The cord is relaxed when the pendulum is vertical (see fig (ii)). The bob is pulled slightly and released. Find the time period of oscillations.

Answer

`(a) 2 pi ((g)/(l)+(k)/(m))^(-(1)/(2)), (b) pi ][((g)/(l)+(k)/(m))^(-(1)/(2))+((g)/(l))^(-(1)/(2))]`