Two identical simple pendulums A and B are fixed at same point. They are displaced by very small angles `alpha " and " beta ( = 2 alpha)` respectively and are simultaneously released from rest at time t = 0. Collisions between the pendulum bobs are elastic and length of each pendulum is l.
(a) What is the minimum number of collisions between the bobs after which the pendulum B will again reach its original position from where it was released ?
(b) Find the time (t) at which B reaches its initial position for the first time after the release.
(c) Write the kinetic energy of pendulum B just after `n^(th)` collision? Take mass of each bob to be m.

Answer

(a) 2, ` (b) t=2pi ((l)/(g))`
(c ) `E=(1)/(2) mlalpha^(2)` g if n is odd and `E=(1)/(2)mlbeta^(2)`g if n is even