Two pendulums with identical bobs and lengths are suspended from a common support such that in real position the two bobs are in contact (figure). One of the bobs is released after being displaced by` 10^(@)` so that it collides elastically head-on with the other bob.
(a) Describe the motion of two bobs.
(b) Draw a graph showing variation in energy of either pendumlum with time, for `0 le t le 2T` , where T is the period of each pendulum.

Explanation

(a) Consider the adjacent diagram in which the bob B is displaced through an angle `theta ` and released
At t = 0 , suppose bob B is displaced by `theta = 10^(@)` to the right , It is given potential energy `E_(1) =E . `Energy of A , `E_(2)=0`
WhenB is released , it strikes A at t = T/4 .In the head - on elastic collision between B and A comes to rest and A gets velocity of B . Therefore `e_(1) = 0 and E_(2) = E ` At t = 2T/4 ,B reaches its extreme right position when KE of A is converted into `PE = E_(2)=E ` Energy of B , `E_(1) = 0 `
At t = 3T/4 , A reaches its mean position , when its PE is converted into `KE = E_(2) =E` . It collides elastically with B and transfers whole of its energy to B . Thus , `E_(2) = 0 and E_(1) = E ` . The entire process is repeated .

(b) The value of energies of B and A at different time intervals are tabulated here . the plot of energy with time ` 0 le t le 2T ` is shown separately for B and A in the figure below .
.