What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity ?

Answer

(a) `sin theta lt theta` ; if the restoring force, `mg sin theta` is replaced by `mgtheta`, this amounts to effective reduction in `g` for large angels and hence an increase in time period `T` over that given by the formula `T = 2pisqrt((l)/(g))` where one assume `sin theta = theta`.
(b) Gravity disappears for a man under free fall, so frequency is zero.