Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position, the two bobs are in constact, . 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 pendulum with time,for `0letle2T` , where `T` is the period of each pendulum.

Explanation

(a) Consdier the adjacent diagram in which the bob B is displaced through an angele `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`. When B is releeased, it strikes A at t =T/4. In the head and A gets velocity of B. Therefore, `E_(1)=0 and E_(2)=0` and `E_(2)=E`. At t=2T/4, B reaches its extreme right position when KE of A is converted into PE=E. Energy of B, `E_(1)=0`.
At t=3/4, A reaches its means position, when in 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`. This entire process is repeated.
(b) The values of energies of B and A at different are tabulated here. The plot of energy with time `0 le t le 2T` is shown separetely for B and A in the figure below.