A simple pendulum has a bob of mass m which carries a charge q on it. Length of the pendulum is L. There is a uniform electric field E in the region. Calculate the time period of small oscillations for the pendulum about its equilibrium position in following cases:
(i). E is vertically down having magnitude `E=(mg)/(q)`
(ii). E is vertically up having magnitude `E=(2mg)/(q)`
(iii). E is horizontal having magnitude `E=(mg)/(q)`
(iv). E has magnitude of E=q and is directed upward making an angle `45^(@)` with the horizontal

Answer

(i) `T=2pisqrt((L)/(2g))`
(ii). `T=2pisqrt((L)/(g))`
(iii). `T=2pisqrt((L)/(sqrt(2)g))`
(iv). `T=2pisqrt((L)/(g))`