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.

Two pendulums with identical bobs and lengths are suspended from a com

1.	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.
Answer» Solution :(a) Consider the adjacent diagram in which the bob B is displacedthrough 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 ` Att = 2T/4 ,B reachesitsextreme right position whenKE of A isconvertedinto `PE = E_(2)=E ` Energy of B , `E_(1) = 0 ` At t = 3T/4 , A reachesits MEAN position , when its PE is converted into `KE = E_(2) =E` . It collideselastically 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 shownseparately for B and A in the figure below . .